Interaction of superstructure, foundation, and soil
by John Joseph Hightower
A thesis submitted in partial fulfillment of the requirements for the degree MASTER OF SCIENCE in
CIVIL ENGINEERING
Montana State University
© Copyright by John Joseph Hightower (1981)
Abstract:
A Fortran computer program is developed, to study the interaction of structural plate elements and their
supporting subgrades. A linear spring (Winkler) subgrade model is used as well as the option of
considering rigid body action of specified areas of the foundation.
Example problems are considered; shear deformation is determined to be a significant contributor to
the deflection profile. Contact pressures are found to agree with pressures predicted by other methods.
Finally, shear stresses and bending moments are shown to accurately represent values obtained by
traditional methods. STATEMENT OF PERMISSION. TO COPY
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INTERACTION OF SUPERSTRUCTURE, FOUNDATION,
AND SOIL
by
JOHN JOSEPH HIGHTOWER
A thesis submitted in partial fulfillment
of the requirements for the degree
•
Of
MASTER OF SCIENCE
in
CIVIL ENGINEERING
Approved:
Chairperson, Graduate Committee
MONTANA STATE UNIVERSITY
Bozeman, Montana
July 1981
iii
ACKNOWLEDGEMENTS
The
Fred F.
and
author wishes
to express
Videon and Dr. Robert G.
contributions
toward
his appreciation to Dr.
Oakberg for their efforts
the
completion
of
this
investigation.
The
author also
instructor,
was
thank Bruce
who originally inspired
responsible
support.
wishes to
for
obtaining
A. Suprenant,
this investigation and
the
required
financial
TABLE OF CONTENTS
SUBJECT
PAGE
V I T A ....................................
ii
A C K N O W L E D G M E N T S .......................
iii
TABLE OF CONTENTS
...................... 0 . 0 .....
LIST OF TABLES ....... .................... .
LIST OF FIGURES
ABSTRACT
iV
V
.....................................
vi.
.............................
INTRODUCTION ......... ............ . ........... .
■ ISOPARAMETRIC FINITE ELEMENTS
....... ............
SUBGRADE M O D E L S .....................................
vii
I
4
14
Integrated Winkler Subgrade .................
Lumped Winkler Subgrade ...................
RIGID BODY A C T I O N ...... .................. ...... . .
RESULTS
15
19
23
...........................
Circular Plate With Point L o a d ...............
Notched Rectangular Plate .. .................
Cantilever Footing Analysis ..................
30
30
33•
36
SUMMARY AND CONCLUSIONS .........................
42
RECOMMENDATIONS ............................
44
REFERENCES .............................
4
APPENDICES
Appendix A:
Appendix B :
Appendix C :
Instructions for Preparing
Input Data ..................
Program listing .................
Cantilever Footing ..............
50
55
84
8
V
LIST OF TABLES
TABLE
PAGE
1
MODULUS OF SUBGRADE R E A C T I O N .......... ..
22
2
SOIL CONTACT PRESSURES
35
.................. .
vi
LIST OF FIGURES
FIGURE
.%
PAGE
I
SIGN CONVENTION FOR PLATE ELEMENT ..........
2
LOCAL COORDINATE AXIS AND NODE NUMBERS
3
CORNER AND MIDSIDE NODE SHAPE FUNCTIONS .... 10
4
NATURAL NODAL COORDINATES
5
TRIBUTARY AREAS FOR CORNER AND MIDSIDE
NODES
6
..... 10
..............
................ . ........... ....... ..
CIRCULAR PLATE:
6
17
20
ELEMENT GRID AND
NODAL N U M B E R I N G .......... ..................
32
7
CIRCULAR PLATE:
DEFLECTION PROFILE ........
32
8
NOTCHED FOOTING:
ELEMENT G R I D .... ...... .
35
9
CANTILEVER FOOTING:
GEOMETRY AND
LOADING ..eeeeeee.eeeeeeee.ee.'. ..... ........ 38
10
CANTILEVER FOOTING:
ELEMENT GRID ..........
11
CANTILEVER FOOTING:
SHEAR FORCE AND
BENDING MOMENT DIAGRAMS— S E C T I O N A L .......
12
CANTILEVER FOOTING:
38
39
SHEAR FORCE AND
BENDING MOMENT DIAGRAMS— TOTAL .............. 41
vii
ABSTRACT
A
Fortran computer
program is
developed, to study the
interaction
of
structural
plate
elements
and
their
supporting
subgrades.
A
linear spring
(Winkler) subgrade
model
is used as well
as the
option of considering rigid
body action of specified areas of the foundation.
Example
problems are considered;
shear deformation is
determined to be a significant contributor to the deflection
profile.
Contact
pressures
are
found
to
agree with
pressures
predicted
by
other
methods.
Finally,
shear
stresses
and
bending
moments
are
shown
to accurately
represent values obtained by traditional methods.
INTRODUCTION
To
a design engineer
structural
that
footing or
the design
The purpose
responsible for the
series of
be done
footings,
it is desirable
easily,
and accurately.
quickly,
of this paper is to
design of a
develop a computer program
to assist the design engineer faced with this situation, and
to investigate
the load response of
a footing supported by
an elastic subgrade.
For
a given
parameters that
footing design
problem there are several
must be considered by
the design engineer.
These parameters include loading patterns,
and allowable
supporting
model
For
the
contact stresses between the
subgrade.
The
the footing and
design,
the subgrade so
small footing
behaves
design it
as
a
the
footing.
the
footing
conditions.
allowed,
To
can
- Since
the
rigid
conservative in the
that a safe footing
is commonly assumed that
body
(1,9) .
Then, by
it is possible to obtain
distribution across the bottom of
obtain shear
then
must accurately
can be produced.
rigid
assuming a linear elastic subgrade,
a linear contact pressure
footing and its
design engineer
satisfying these parameters,
footing
size limitations,
be
forces and bending moments,
analysed
deformation
footing
of
model
using the equilibrium
the
footing
will
tend
is
to
not
be
estimation of contact pressures between
2
the footing and the
contact
subgrade.
stresses may require
the construction of the
due
The conservative estimate of
to
the
greater
more materials to
be used in
footing than is necessary.
area
of
footing
This is
required to reduce
contact stresses to an allowable value.
This
paper
modelling
will
examine
the footing
the
footing
as
subgrade
a
models
linear spring
If
as
an
such
as
(Winkler)
to account
than the rigid footing
This is accomplished by
elastic
body.
. Due
the
this
contact
deformation.
capability
to
and the
computational
or Pasternak, a
subgrade model is used.
the footing
for changes
occurs
is allowed,
it becomes
in the footing stiffness
will
To approximate
to model
material
Boussinesq
caused by foundation walls or c o l u m n s .
where
accurate method of
analysis costs of more representative
deformation of
necessary
model.
deformable
difficulties and high
subgrade
more
and subgrade
and linear elastic subgrade
modelling
a
Areas of the footing
experience
little or no
the increase in stiffness, the
foundation walls . or columns
as rigid
bodies is considered
Foundations
displace
loading
supported
uniformly
over
the
by
downward
entire
a
when
surface.
Winkler
subgrade
subjected
This
will
to a uniform
response is not
3
reflective
this
of true
program
is
combined footings.
soil behavior.
limited
to
the
Therefore,
analysis
the
use of
of spread and
ISOPARAMETRIC FINITE ELEMENTS
The finite element
on
the
eight-node
Hinton and
computer program developed is based
quadrilateral
Owen, 1977, developed a
B O K l , based on this element
basis
for the
paper.
isoparametric
(5).
footing analysis
element.
plate analysis program,
This program is used as a
program developed
in this
BOKl includes the effects of shear deformation,
thus
allowing the analysis of thick plates.
For
the development of
BOKl the following assumptions
are made:
1)
The deflections of the plate are small.
2)
Normals to the midsurface before deformation
remain straight but not necessarilly normal
to the midsurface after deformation.
3)
Stresses normal to the midsurface are negligible
■irrespective of the loading.
The
perhaps
method
complete
development
the
and
most
is
of
the
important
displayed
documentation
of
element
aspect
here
the
as
stiffness matrix is
of the finite element
taken
program
from
(5).
For
and the theory of
5
isoparametric elements,
the reader is refered to
(5).
Development of the Element Stiffness Matrix
For the derivation of the stiffness matrix the following
notation is used,
(The sign convention for
this element
is illustrated in Fig. I).
$
= displacement vector
w ,ex ,ey
= components of 6
(including shear deformation)
M
= . vector of bending moments
m x ,my ,mxy= components of M
Q
=
vector of shearing forces
q x ,qy
= components of Q
X
= vector of bending
deformation
xx ,xy ,Xx y = components of bending deformation
0
X x rXy
Additionally, the
= vector of curvatures due to shear
=
components of
following relationships are established:
j
'
i
6
Y
SIGN CONVENTION FOR PLATE ELEMENT
FIGURE I
7
6 = \eY> = <3 w/3 x
9 w/9 y
Q
+ /x
+
\
x
I
XI
X = <x
I -9ex/9x
I
r
—96y/3 y
- (9
/9 y
+ 9©y/9 x)'
The total potential energy of the element is given by
'If = 0.5 U m xX x + ntyXy + m xyxXy + qx^
+ Qy^ery )dA - \qwdA
^
I
The stress-strain relationships may be written as
M — D fX
0 = DgJgT
(I)
8
where D f is the matrix of flexural rigidities and D g is the
matrix of shear rigidities and are defined as follows:
I
Df =
D5 =
Et V (12 (1 - v 2) )
Et /(2.4 (1+v) )
0
0
1
0
0
0
(1-v)/2
I
0
0
I
Substituting the stress strain relationships into eg.
(I)
yields
= 0.5 \( [XJtD f [X] + IeffDs ^ ] )dA - \ qwdA
)A
zA
For
isoparametric
expressed by
formulation,
the same function as
element
shapes
are
the assumed displacement
field and are expressed as
X
(2 )
j l
N im
yJ
9
and
8
G = E N i [I]Si'
i=l
where
Ni is
the element
where
Si =
[w ir e Kir 6 Yi1
shape function
for the ith node.
The element shape functions are
Ni = 0.25(1-Cn
-£2n 2n +
C n 2+ T1 2 )
N2 = 0.50 ( 1 - n - £ 2+ £ 2n)
N3 = 0 . 2 5 (-I - Cn +C2- £ 2n+£n2+ n 2)
N4 = 0.50 (I +C - C n 2- O 2)
(4)
NS = 0.25 (-1 +Co +C2n+Cn2+ n 2)
N6 = 0.50(1 +n - C 2“ C2n)
N7 = 0.25 (-1 -Co +C2+C2n-Cn2+ n 2)
NB = 0.50(1 -C +Cn2- O 2)
£ and
by
n are l o c a l , natural
Fig. 2.
equaling
The
1.0 at
0.0 at all other
and
midside node
3 (a,b) .
coordinate axis as defined
shape functions have
their corresponding
nodes.
the charateristic of
node, and identically
The characteristic shape of corner
shape functions
are illustrated
in Fig.
10
LOCAL COORDINATE AXIS AND NODE NUMBERS
FIGURE 2
FIGURE 3
11
The
lateral
strain-displacement
relationship
for the quadri­
isoparametric element under consideration is
E=
8
£ Bi 3i
i=l
where
t_t
t
[Er = [ [ % ] , [ # ] ,
and
0
- %Ni/bx
0
[Bi] =I B fi
0
0
- %Ni/%y
- &Ni/^y
2>Ni/<bx
&Ni/%y
-
0
- %Ni/ox
Ni
0
0
-Ni
To assemble the strain matrix it is necessary to obtain
the derivatives
of the shape functions
cartesian coordinate
system.
To do this
with respect to the
the chain rule of
differentiation is used
&Ni/&x = (^Ni/BC ) (d£/dx)
+ (%Ni/%n)(5n/&x)
(5)
12
Q N i / by =
or,
( QNi/BC) ( H / Q y )
+ ( QNi/'dn) ( Q n A y )
in a matrix formulation
^QNi/Qx I
QS/%x
QS/Qx
QNiASj
I9Ni/Qyj
QC/Qy
1QnZQy
)QNi/Qn(
(7)
inverting this matrix yields
QNi/QCj
/QNi/Qnl
QxAS
Qx/Qn
where the matrix
QyAs
Qy/Qn
r&NiAxj
>
IQNiAyJ
=
f%Ni/%x)
[J]{
>
IjsNi/Qyj
(8)
[J] is known as the Jacobian Matrix,
To evaluate the Jacobian it is necessary to determine
the
values of Qx/QS, QyA Se Q x A n r and QyAn •
Different­
iation of eg. 2 yields
Qx/QS=
8
2 (QNi/QS)x.+ N i (Qx. A n )
i=l
since x
is a constant,
1
1
Qx/QS = 0.0, this yields
13
S x M =
8
Z (a.Ni/8g)x.
i=l
1
(9)
a similar proceedure is used to evaluate d y / d C , % x/an , and
5y/&n.
When
i>.x/d£,
determinant
dy/d'|,
of the
.9.x/dn,
and
Jacobian Matrix
&y/%h are known, the
is evaluated.
If the
determinant is less than or equal to zero, there is an error
in
the coordinate
mapping proceedure
and the element grid
selected must be reviewed .for errors.
Once the Jacobian is
known,
the
it
is
inverted
to
obtain
shape
function
derivatives required in the assembly of the strain matrix.
To . obtain the
element stiffness
matrix the following
function must be evaluated:
[k] = ^[B1I [D] [B]dA = ^ [ B ] [D] [Bjdet[J]d£dn
(10)
To integrate this function a numerical method known as Gauss
Quadrature is used.
gauss points)
to
the
or a 3 X
user.
presented in
The option of using either a
A
(4,5).
3 (9 gauss points)
review
2 x 2 ( 4
rule is available
of this integration technique is
SUBGRADE MODELS
Since 1867 when E.
as closely spaced,
Winkler modeled an elastic subgrade
independent springs, numerous models for
subgrades have been developed.
advanced models is based
point
load
include:
bonded
on
ah
to
Hetenyi,
its
upon the Boussinesq equation for a
elastic
Pasternak,
a
surface
that
can
Filonenko-Borodich,
membrane bonded
consists
half
that
can
(3).
with a
deflect
Other models
plate element
only in shear;
a plate element bonded to its
deflect
a
only
Winkler
model
to its surface; a
of a Winkler
space
Winkler model
a Winkler model with
surface
The most common of the more
in
with
bending;
a
stretched
Generalized model, which
model with the
additional aspect of
moment terms proportional to the rotation of a point
Due to computational difficulties encountered,
Winkler model will be
exerted
is linearly
considered.
(6).
only the
For this model the force
proportional to
the deflection of the
subgrade.
Two
methods
considered.
of
modelling
The first is
the
Winkler
subgrade are
a more precise method of actually
integrating an assumed displacement field over the elemental
area.
each
The second
node, which
matrix.
is to
"lump" the
result in
subgrade stiffness at
I
a diagonal
subgrade stiffness
15
Integrated Winkler Subgrade Model
The proportionality constant
commonly
denoted
as
reaction".
For
assume
displacement
a
displacement
element.
the
B,
or
"the
integrated
modulus
model
field,
field used is
The
for a Winkler subgrade is
of
subgrade
it is necessary to
For consistency
the same as
the
used for the plate
assumed displacement field for
a given point
on the element can be described by the function
w
=
U1 + S2 C + a3n + a4 C 2 + Bg Cn + a6n 2 + B7V n + a^Cn2 (11)
or, for the entire subgrade element
8
w
=
1
where
E fU
i=l
,n.)a
£lc.,n i ) = [l E1 H1 q
The
local nodal
illustrated
in Fig.
(12)
1 1
Ei-Ii n? E^n1 Ci-I= I
numbering scheme
4.
Substituting
and coordinates are
the nodal coordinate
values for £ and n into the matrix F(£,n)
where
16
8
F(Cm)
=
Z [ f ( C. m. )]
i=l
1
(13)
1
yields the following matrix:
I
-I
-I
1
1
1
1 0 - 1
0
0
1 1 - 1
I
-I
1
1
0
I
0
0
1
1
1
I
I
1
0
0
1
1 - 1 1
0
-I
1 - 1 0
1
0
1
0
To solve
1
for the
-I
-I
0
0
-I
I
1
0
1
0
1
0
0
1 1 - 1
0
0
0
unknown constants it is
to invert the above matrix.
This yields
necessary
17
(-1,1)
(0,1)
(1,1)
NATURAL NODAL COORDINATES
FIGURE 4
18
m
-0.25
0.50
0.00
0.50
0.00
0.00
0.00 -0.50
0.00 -0.50
0.00
0.00
0.00
0.50
0.00
0.00
0.25 -0.50
0.25
0.00
0.25 -0.50
0.25
0.00
-0.25
0.00
0.25
0.00
-0.25
0.00
0.25 -0.25
0.25
0.00
0.00
0.00
0.25
0.00
0.50
O
I
0.00
Multiplying
m
0.00
CN
0.25
I
O
to
Ul
0.50
the
CN
O
I
0.50
-0.25
-0.25
0.00
0.25 -0.50
0.25 -0.50
above
matrix
yields the shape functions
0.25
by
0.00
-0.25
0.50
0.25 -0.50
0.25
0.00
-0.25
0.50
the displacement vector
recorded earlier
(Eq. 4).
Using
the potential energy of the subgrade
U = 0.5
LwdA
(14)
'
a
the following relationship is e stablished:
[k]
U N J t [NJdA
\ [NJt [N]det[J]dCdn
Ia
4%
The values for the shape
point)
the
are computed
determination of
(15)
function at a given point
in the
subroutine STIFPB.
the subgrade
(a gauss
This makes
stiffness matrix by the
19
integrated method an easily implemented proceedure.
Lumped Winkler Subgrade
A
model.
whose
simpler version of
This
terms
modulus, B r
the Winkler model
model consists of a
are
evaluated
by
To establish the values
diagonal stiffness matrix
multiplying
by a tributary area
is the lumped
the
subgrade
associated with each node.
of the tributary area the following
empirical derivation is presented:
1)
Divide the plate area into sections as shown
in Fig. 5a and compute the tributary areas
to be associated with each node.
2)
Rotate the element 90°
and repeat the first
step, Fig. 5b.
3)
Sum the tributary areas for each node given
in steps I, and 2 and divide this sum by 2.0.
This gives an approximate tributary area to
be associated with each node. Fig. 5c
20
1/12
1/12
1/4
1/12
I/] 2
1/4
1/12
1/12
1/12
1/6
1/6
1/12
TRIBUTARY AREAS FOR CORNER AND MIDSIDE NODES
FIGURE 5
21
This yields
tributary stiffnesses of
for
nodes,
corner
nodes.
and
Since the area
(1/6)
(1/12)
times
times the area
the area for midside
is computed in the subroutine STIFPB
the addition of this option is also easily accomplished.
The
critical
selecting a
factor
in
using
value for the subgrade
represents the
subgrade.
the
Winkler model is
modulus that accurately
Table I gives
some guidelines to
follow in the selection of the subgrade modulus.
realized
that.this
table cannot
It must be
override the necessity of
performing an analysis of the subgrade to be used.
22
SUBGRADE MODULUS, B , Kips/cubic inch
I
I
100
_____ I_-
r
I
150
200
I
250
I
500
I
4
General soil rat ing as subgrade,subbase or base
Very poor
subgrade
Poor
subgrade
Fair to good
subgrade
G-Gravel
S-Sand
M-"Mo",very fine sand,silt
C-Clay
F-Fines,material less than
O .Imm
O-Organic
W-Well graded
P-Poorly graded
L-Low to medium compressibili tv
H-High compressibility
ML
^
OH
CL
OL
>
MH
TABLE I
Best
subgrde
Good
subbase
Goodpest
baseoase
GW
I
SW
I
RIGID BODY ACTION
Areas
of
foundation
the
walls
deformation.
stress
require
the
could
of
in
this
be
a
the
used.
require
matrix
This
Then,
translated
in
order
to
stiffnesses
expansion
a
40
added
ill-conditioned
x
to be condensed or
to
the surface of
would have to be
freedom would have to be added
to
of
40
The
terms to the neutral axis of
properly
of the plate . with those of
the
no in plane
stiffness matrix.
rigid body translations
Axial degrees of
or
modification would
an equivalent stiffness along
plate
matrices
or
columns
action . a plane strain/plane
implemented to translate these
to
with
little
the entire wall would have
translated to
the plate.
contact
experience
model
use
stiffness of
the plate.
will
To
element
footing
the
the wall.
plate
matrix.
the
merge the stiffness
stiffness matrix
very stiff compared to the footing.
elemental stiffness
Also,
system
This would
the
will
if the
additional
result
in
an
wall or column is
This leads to numerical
problems in obtaining the solution.
A
simpler
method
of
modelling
foundation walls and
columns is to treat them as pure rigid bodies.
the
degrees of
rigid body
freedom for
to a total of 3.
all nodes
This reduces
in contact with the
To incorporate the rigid body
modes into the program it is necessary to identify all nodes
24
on a
given rigid body.
stiffness
matrix
Thenf
into
the
before merging the elemental
global
matrix,
the elemental
matrix must be transformed to reduce the degrees of freedom.
The
number of
(3(8-N)
degrees of
+ 3) where N is
a rigid body.
freedom for
an element
will be
the number of nodes in contact with
It is important to understand the development
of the transformation matrix.
From basic
relative
engineering mechanics it is
velocities of
two points
on a
known that the
rigid body can be
expressed as
V
This
B
= V
A
expression
eliminating
relating
a
+ 0 x r
X
can
time
(16) ,
B/A
be
integrated
dependency,
relative displacements
to
with respect to time,
achieve an expression
of two
points on
a rigid
body.
W
B
= W
A
+ 0 x r.
B/A
Expanding this expression
gives
(17)
by putting it into component form
25
w -
W - + (e r + © _) x
kB
Xi
yj
kB
(r - + r
xi
_)
yj
B/A
W k B + r Y (Gxk) “ r Xx (© yk)
w
For
not
a
A
+ r e
Y x
- r e
plate bending applications
statical
sign
(18)
x y
convention.
the sign convention is
To
modify
eq. 18 the
following change in variables must be implemented
e
e
x
y
=
e
y
= -e
x
This change in variables yields
w
B
= w
A
+ r e
x
x
+ re
y
y
(19)
Rotations of any point A will be equivalent to the rotations
of
a
reference
displacement.
point
B
In matrix form,
since
it
is
a
rigid
body
the relative displacements of
two points on a rigid body can be expressed as
26
I
r
r
x
To
y
O
I
O
O
O
I
(20)
develop the necessary
modifications to the program
the following relationships will be u s e d :
where
the
{5 }
is the elemental displacement
system displacement
modes.
Characteristics of
follows:
vector with
v e c t o r , and (D) is
respect to rigid body
the transformation matrix are as
27
(Fe) = [ke](6 )
but
(S)
= (T)(D)
The strain energy of the system becomes
u = 0.S(S)Ike) (S') = 0.5 { D Ji(T)Ike) [T] (D)
(21)
This results in a transformed stiffness matrix
[k) = (T)Ike)(T)
(22)
The total displacement formulation then becomes
(F) = [TJi(Fe) = (T)iIke] (T)(D) = [k]{D)
To avoid formulating
requiring
2
stiffness
transformation,
those
N3
that require
assembly
columns of
modification.
of the
operation it
the entire transformation matrix,
multiplication
rows and
(23)
it
operations
to
is convenient
the elemental
This is easily
global stiffness
matrix.
is necessary to identify
perform
the
to modify only
stiffness matrix
done during the
To perform this
which,
if any, nodes
28
on
an
element
element
are
in
is determined
contact
with a rigid body.
to contain
nodes in
If an
contact with a
rigid body the following sequence of events will occur
1)
The x and y distances from a reference node
to the first node of the element in contact
with a rigid body will be calculated.
2)
The transformation matrix will be formulated;
rows of the elemental matrix corresponding to
the node under consideration will be pre-mul-
3)
tiplied by
t
[T]; the columns will be post-mul­
tiplied by
[T] .
The next node on the element in contact with a
with a rigid body will be sought out and the
operation will be repeated.
4)
All 3 x 3
sub-matrices corresponding to 2 nodes
in contact with the same rigid body will be
overlayed i n t o .the same 3 x 3
the diagonal
set to
0
.0 ).
sub-matrix along
(their original positions will be
29
5)
If the element is in contact with more than one
rigid body the above proceedure will be repeated
for all rigid bodies in contact with the element.
6
)
The merging of the elemental matrix into the
global stiffness matrix will continue as if
no modification has occured.
It
is necessary to
when using the rigid
of
a column
or wall
use a certain
body option.
is similar
amount of intuition
Obviously,
if the height
to the footing thickness,
I
little
realized
or no effect
of their additional
by the footing.
stiffness will be
In this instance
assumption will give an erroneous solution.
the rigid body
RESULTS
The finite element program yields three quantities that
are
of
primary
deflections,
concern
subgrade contact
the footing i t s e l f .
to
document the
The
load
to
three problems include:
eccentric
user.
These
include
stresses, and stresses within
Three verifiable problems are analysed
accuracy of
at the center,
the
the finite
element solution.
a circular plate
a notched rectangular
column load,
and a
with a point
footing with an
cantilever footing
with two
column l o a d s .
Circular Plate With Point Load
The first
point
problem analysed is a
load at the
circular plate with a
center supported by
a Winkler subgrade.
This problem was solved exactly, using thin plate theory, by
Timoshenko
1981,
and W o inowsky-Krieger, 1959,
solved a
similar problem
deflections
A.C. Ugural,
using a two-parameter Ritz
solution
(8 ).
solution,
the Ritz solution, and the finite element solution
are compared,
The
(7).
predicted
and their differences analyzed.
The problem parameters are given as
I =
(D/Bj3 = 5.0
(7)
by
the
exact
31
P =
(0.00102) (S
D = E t 3 / (12( I
tt
B I 3 )
- V 2 )
where
D = plate bending stiffness
B = modulus of subgrade
E = Youngs modulus of elasticity
v = Poissons ratio
P = magnitude of the point load
In order to minimize the cost of analysis, advantage of
symmetry
is taken
analyzed.
normal
grid
to
and
illustrated in Fig.
the
nodal
6
.
three methods of
a
solution.
very
This result
selection of the
finite
or
Y axis is allowed.
scheme
selected
The
is
a radial axis predicted by the
The two-parameter Ritz solution
solution
is not
when
compared to the exact
unexpected due
assumed deflection function.
element solution also
exact solution.
plate is
Fig. 7 illustrates a comparison of
analysis.
poor
X
of the
then, are that no bending
numbering
the deflection profile along
yields,
one quadrant
The boundry conditions,
deformation
element
and only
to the poor
However, the
varies significantly from the
This difference is attributable to shear
32
I
Y
CIRCULAR PLATE - ELEMENT GRID AND NODAL NUMBERING SCHEME
FIGURE 6
9.0
Finite element
0.004
Iution
0.008
-Parameter
z solution
0.012
Exact so lution
0.016
0.02 0
CIRCULAR PLATE: DEFLECTION PROFILE
FIGURE 7
(INCHES)
10.0
33
deformation.
Classical theory
shear deformation
thickness to
This is
plate
suggests that the effects of
are negligible if the
the radius of the plate
is less than
reflected by the finite element
with
no
deformation is
supporting
ratio of the plate
0 . 4
(7 ).
solution of a thin
subgrade.
However,
predicted to be significant
shear
for thin plates
supported by a Winkler subgrade.
A
significant difference is
deflection
profiles
predicted
apparent in examining the
by
the
exact
compared to the finite element solution.
predicts positive curvature
bending moments
reflected
element
by
the
solution
finite
predicts
in negative moments.
moments
element
This behavior is not
sol u t i o n . .
The
finite
negative,
or reverse curvature
of the plate.
This profile results
Obviously,
predicted
The exact solution
therefore, positive radial
along a radial axis.
toward the outside edge
the
and,
solution as
is
an
the difference in signs of
important one to the design
engineer responsible for the safe design of a footing.
Notched Rectangular Plate
The
second
problem
contact pressures predicted
solved
is
used
to
verify soil
by the finite element solution.
34
A solution
compared
Bowles,
for a notched rectangular
to the solution
1977,
grid used
(I).
plate is presented as
for a similar
The footing
geometry and
is illustrated in F i g e
inches was selected in order
plate presented by
8
,
the element
A footing depth of 24
to insure a minimum of bending
deformation.
The loading is eccentric to the mass center of
the
therefore,
This
footing;
insures
that
the
an overturning
the
contact
corners
of
footing
present
under the footing.
predicted pressures
the
corners
rigid
of
footing
including
solution
will
stresses
at
the outside
bound the contact pressures
Accordingly,
the comparison of
will be restricted to
the pressures at
the
footing.
analogy
(I),
shear
moment will exist.
deformation)
predicted by
The results predicted by a
finite
element solution
(I),
the program
(not
and the finite element
developed in this paper
are shown in Table 2.
The
compare
results predicted by
favorably
with
each
the finite element solutions
other,
certainly within the
difference to be expected by considering plates of different
thicknesses.
Also,
expected
to
due
a
shear
small
degree
of variance is to be
deformation.
H o w e v e r , the finite
element solutions vary significantly from the solution
35
1 0 .0 '
56
I
43 :
9
'
®
,
62
• 6,o ,
8
5II
.
«
.
:
__
^
.
©
35 ,
'I
,
'37
©
.
' ®
,21 .
'
, 1Z J
'©
'
31, , .33,
©
— •—
I
©
S>
©
©
51
'49 t
§ ;
- :
®
I
I
'
I----- 9----- 1— e— IH H --- •----1
9
3
5 7
1 0 .0 '
NOTCHED FOOTING: ELEMENT GRID
FIGURE 8
SOIL CONTACT PRESSURES: KSF
NODE
FINITE ELEMENT
RIGID BODY
BOWLES
PLATE
BOWLES
I
5.49
5.308
4.27
9
5.43
5.287
5.57
49
5.71
5.755
6.51
51
5.62
5.602
6.90
56
5.44
5.292
5.84
62
5.66
5.655
6.75
TABLE 2
36
predicted by
finite
the rigid footing analysis.
element solution predicts
stresses
than
primarily to
the
rigid
As expected, the
much more uniform contact
footing
the relief of contact
analogy.
This
is due
stresses resulting from
bending in the plate and a corresponding increase in contact
stresses
in
low
pressure
areas.
include a maximum allowable
rigid
footing solution
this,
requiring a
The
finite
distribution
pressure.
that
This
contact stress of 6.0 ksi.
predicts stresses
larger footing
element
solution
nowhere
would
The problem parameters
The
much higher than
to distribute
the load.
however, predicts a pressure
exceeds
require
the
maximum allowable
neither re-solution of the
problem nor additional materials for the footing.
Cantilever Footing Analysis
Wang
cantilever
and
Salmon, ' 1979,
footing using
finite element solution of
solve
a rigid
the
problem
beam assumption
of
a
(9).
A
the problem is presented and the
solutions compared as a final example.
Problem geometry and
parameters are illustrated in
Since the footing is
symmetric
about the
need be analysed.
Fig. 9.
X-axis, only
This use
one half
of the footing
of symmetry reguires the use of
37
boundry conditions constraining
along
the
X-axis.
The
illustrated in Fig. 10.
rotation in the Y direction
finite
element
grid
used
is
A listing of the computer solution
for this problem is given in appendix C.
The
finite element solution
bending
moments
in
terms
of
solutions with those predicted
is necessary to sum the
given
points
along
the
presents shear forces and
a
unit
width.
To compare
by the rigid beam analogy it
bending moments and shear forces at
X-axis.
Fig. 11 illustrates the
bending
moments and
shear forces
predicted by
element
solution at
selected points
the finite
along the X-axis.
By
computing the approximate areas
under each of these curves,
moment
the footing
are developed,
are compared with
the moment and
Fig.
and shear
12.
diagrams for
These diagrams
shear diagrams
resulting from the rigid
diagrams developed from
closely with their
beam analogy.
The
the finite element solution compare
counterparts.
rigid columns and adjacent areas
Bending moments under the
are close to zero since no
bending is allowed to occur in these areas.
38
2 1 1-10
Z
CO
I— I
6'-8"
^ I'-2"
I'-2"
w
4'-6"
^
ET
13'-6"
lO'-S"
I
? !
7'-4"
I '-O"-—
1 2 '-9 ;
5'-E
.
---------- ►
196 kips
333 kips
CANTILEVER FOOTING: GEOMETRY AND LOADING
FIGURE 9
Y
i
i
I
— e— II
— e— i
'CD <
%
I
I
—
^
.
!
rV
? ^:
ELEMENT GRID
FIGURE 10
I
--- e-- 1
O -'0
0
■- F * — •— I' : r
'
<
— •— I
'
— •— iI
•—
©
<
.
%
39
i
;
i
2A=-27'k
-74'k
2A=+146’k
• 2A=+140'k
CANTILEVER FOOTING: BENDING MOMENT DIAGRAMS— SECTIONAL
FIGURE Ila
40
CiL
Cl
/I
2A=-142k
2A=-35k
CU
2A=0k
________ I
2A=80k
2A=-40k
CANTILEVER FOOTING: SHEAR FORCE— SECTIONAL
FIGURE lib
41
196 kips
1 333 k i p s
Plate
Rigid Footing
SHEAR FORCE DIAGRAM— TOTAL
Plate
Rigid Footing
BENDING MOMENT DIAGRAM— TOTAL
FIGURE 12
SUMMARY AND CONCLUSIONS
This paper
method
use
presents an overview of
application to footing
of
the
studied.
plate
eight-node
analysis.
isoparametric
The modification
of a
analysis program, B O K l ,
Winkler subgrade
the finite element
Specifically,
plate
element
the
is
documented finite element
to include the
and rigid body action
effects of a
of foundation walls
and columns is discusbed.
Selection of the Winkler
is
used
based on
in
limitations of
solving
the
technique requires the
to maintain its
of
model to represent a subgrade
the frontal solution technique
displacement
The frontal
use of elemental stiffness matricies
efficiency.
more andvanced
formula.
For an accurate representation
subgrade models,
elemental matrices are
difficult to generate.
It
is
stiffening
footing.
considered
to
effects of columns
A rigid body
to avoid numerical
the rigid
reference
node.
desirable
and walls in
instability problems.
body to
After
to
model
the
contact with a
model is selected for efficiency and
reduction of the degrees of
with
be
This requires the
freedom of all nodes in contact
the three
degrees of freedom of a
deflections
are
calculated
the
translations of the reference node deflections to eliminated
nodes is accomplished by rigid body relations.
43
Shear
deformation is determined
contribution
to
the
Winkler subgrade.
total
to have a significant
deformation
This appears to be
of
a
plate on a
true even for plates
that would be considered as thin plates in classical theory.
This
is
important
to
a
design
engineer
because of the
possible difference in sign of the bending moments predicted
by thin plate analysis
The
importance
of
as compared to thick plate analysis.
including
shear
deformation
is
most
prominent under a point load.
Soil contact pressures
from those
contact
are shown to vary significantly
predicted by a rigid
stresses predicted
footing analogy.
by a
rigid footing analogy are
"relieved" by allowing bending in the footing.
in a
possible savings of materials
The high
This results
needed to construct the
footing.
Shear
stresses
and
bending
finite element method agree
a more
moments
approximate method
or
shears
at
a
moments predicted by the
closely with those predicted by
(9).
given
Due to
cross
the profiles of the
section
it may be
possible to vary the spacing of the reinforcement to realize
some savings in material.
RECOMENDATIONS
Perhaps the most important modification to the computer
program developed is the addition of the ability to use more
advanced subgrade models.
This alteration would require the
modification of the solution
calculating
global
routine to include a method of
stiffness
degrees of freedom required
Perhaps the
to
addresses
for
by the subgrade model selected.
simplest method of accomplishing
formulate
the
Unfortunately,
this
entire
would
additional
global
require
this would be
stiffness
matrix.
large increases in the
required memory resources as well as the cost of analysis.
For a much
program
more accurate and theoretically significant
the addition
of a
employed.
This
structures,
including the analysis
This
also
would
would
viscoelastic subgrade
allow
allow
the
the
analysis
various
of foundations on snow.
accurate
settlement of large structures
of
could be
prediction
of
the
which is also of interest to
the design engineer.
Ultimately,
the addition
implemented.
if a large computer system were accessible,
of a three-dimensional frame
This,
combined with
program could be
a viscoelastic subgrade,
would allow the study of structure behavior over a period of
years,
thus
problems,
allowing
the
study
of
earthquakes,
and other time dependent loading patterns.
fatigue
45
On
a
more
immediate
modifications that
would be of Value
One very real problem with
large
volume
of
information is,
added
information
deflections,
of the
total . stresses
yielded.
enable
moment
the
would
data.
Also,
This vast bulk of
to interpret.
The
vastly
simplify
the
the ability to compute
moments .at a given cross section
design
and shear
several
contour mapping of stresses,
etc.
and
are
to a design engineer.
at best, very difficult
interpretation
would
there
a finite element analysis is the
capability of graphical
moments,
the
level,
engineer
diagrams much
to visualize the total
easier, thus allowing some
insight as to the behavior of the footing.
To
eliminate shearing deformation,
analyze an extremely thin plate.
analyzed is
a
apparent.
numerical
Since the flexural
for
inversly
proportional
greater
of 0.02.
instability
constant
thickness.
The circular plate problem
subject to shear deformation
thickness to radius ratio
this
it is necessary to
the
The
than
ill-conditioned
problem,
to
the
in
program
term
square
shear
To
the
becomes
rigidity of the plate is left
the
flexural
matrix.
For plates thinner than
shearing
resulting
for plates with a
of
increases
the
stiffnesses
rigidity,
minimize
change
are
in
become much
resulting
in . an
the effects of this
46
instability recompiling the program with a. double precission
option is
necessary.
be done.
For very
modulus of
changed
Beyond this there
is little that can
thin plates with an extraordinarily high
elasticity,
slightly,
solutions in which
and
the flexural
the thickness is
rigidity held constant
should be run as a stability check,
A final important
is
the
ability
whenever
occur
a
to
modification that should be included
modify
state , of
whenever
outside
the
analyze
this
the
kern
uplift
of
the
problem,
subgrade stiffness matrix
occurs.
resultant
of
This condition will
the
footing.
The
allowed to bond to the
to pull
the
loading is located
In order to correctly
subgrade
material must not be
footing as this suggests the ability
the footing down.
This
modification would require
the inversion of the subgrade stiffness matrix to obtain the
flexibility matrix.
Once the flexibilty matrix is obtained,
the rows and columns of the matrix that correspond to a node
in
must
uplift would
have to
be re-inverted
(2),
The
problem
correct
solution.
routine
and
justifiable
the
be set
to obtain
then
must
to zero.
a modified stiffness matrix
be
The additional
extra
before
computer
this
The matrix then
resolved
to obtain the
expense of the inversion
time
solution
would
package
have
to be
should
be
47
implemented.
Further study
rigid
body
footing.
wall
action
is needed on the
of
Particularly,
or column height
established.
columns
yield a good solution.
and
limiting values
to the footing
This limiting value
for which rigid body
effects of considering
walls
contacting the
of the ratio of the
thickness need to be
would be the lowest ratio
action could reasonably be expected to
REFERENCES
Bowles, Joseph E., 1977, FOUNDATION ANALYSIS
AND DESIGN, McGraw-Hill Book Company, New
York, 750 pp.
Cheung, Y. K. and Nag, D. K., 1968, PLATES
AND BEAMS ON ELASTIC FOUNDA T IONS-LINEAR
AND NON-LINEAR BEHAVIOR, Geotechnique,
V o l . 18, 250-260.
Cheung, Y 0 K..and Zienkiewicz, 0. C., 1965,
PLATES AND TANKS ON ELASTIC FOUNDATIONS
-AN APPLICATION OF THE FINITE ELEMENT
METHOD, International Journal of Solids
and Structures, Pergamon Press L t d . ,
Great Britain, V o l . I, 451-461.
Cook, Robert D., 1974, CONCEPTS AND APPLICATIONS
OF FINITE ELEMENT ANALYSIS, John Wiley and
Sons, New York, 402 pp.
Hinton, E. and Owen, D. R. J., FINITE ELEMENT
PROGRAMMING, Academic Press, London, 305 pp.
Kerr, Arnold D., Sept. 1964, ELASTIC AND
VISCOELASTIC FOUNDATION MODELS, Journal
of Applied Mech a n i c s , Transactions of
the A S M E , 491-498.
Timoshenko, S. and Woinowsky-Krieger, S.,
1959, THEORY OF PLATES AND SHELLS,
McGraw-Hill Book C o m p a n y , New Y o r k , '
580 pp.
U g u r a l , A. C., 1981, STRESSES IN PLATES
AND SHELLS, McGraw-Hill Book Company,
New York, 317 pp.
49
9
Wang, Chu-ICia and Salmon, Charles G.,
1979, REINFORCED CONCRETE DESIGN
3rd. e d . , Harper and Row, New York,
918 p p .
Appendix A
Instructions for Preparing Input Data
CARD SET I — PROBLEM C A R D (15)-one card
Cols. 1-5
NPROB
Total number of problems
to be solved in one run.
CARD SET 2— SUBGRADE TYPE (15) -one card
Cols. 1-5
IFND
Type of subgrade modeled
0 =no
subgrade
I=Iumped Winkler
2=integrated Winkler
CARD SET 3- -TITLE CARD(18A4)-one card
C o l S z 1-72
Title
Title of problem-limited
to 72 alphanumeric
characters
CARD SET 4- -CONTROL C A R D (1215)-one card
C o l S . 1-5
NPOIN
Total number of nodal
points.
6 - 1 0
NELEM
Total number of elements.
11-15
NVFIX
Total number of restrained
boundary points-where one
or more degrees of freedom
are restrained.
16-20
NCASE
Total number of load cases
to be analysed.
21-25
NTYPE
Blank
26-30
NNODE
Number of nodes per element
(= 8 )
31-35
NDOFN
Number of degrees of freedom
per node (= 3).
36-40
NMATS
Total number of different
materials.
41-45
NPROP
Number of independent
properties per material
(— 4)
46-50
NGAUS
Order of integration formula
for numerical integration
(2 or 3)
51-55
NDIME
Number of coordinate
dimensions (= 2 ).
56-60
NSTRE
Number of independent
51
generalized stress
component (= 5)
CARD SET 5— ELEMENT CARDS-One card for each element.
Total of NELEM cards (see Card Set 4)
Cols. 1-5
NUMEL
Element Number
Material property number
6-10
MATNO(NUMEL)
11-15
LNODS(NUMELfI)
1st Nodal connection
number
46-50
NOTE:
L N O D S (NUMEL f8 )
8 th
Nodal connection
number
The nodal connection numbers must be listed in
an anticlockwise sequence, starting from any
corner n o d e j the element being viewed from
above the plane z = 0 .
CARD SET
— NODE C A R D S (15f2 F 1 0 .5f15)-One card for
each node whose coordinates are to be
input.
Cols. 1-5
IPOIN
Nodal point number
6-15
C O O R D (IPOINfI)
x-coordinate of node
16-25
C O O R D (IPOINf2)
y-coordinate of node
26-30
NDTYP
Type of node
1 = corner
2 = midside
6
NOTES: The coordinates of the highest numbered node
must be in p u t f regardless of whether it is a
midside node or not
The total number of cards in this set may
differ from NPOIN (see Card Set 4) since
for element sides which are linear it is
only necessary to specify data for corner
n o d e s ; intermediate nodal coordinates being
automatically interpolated if on a straight
line.
52
If a type one Winkler model is used all
nodal coordinates must be specified since
it is necessary to identify the node type.
CARD SET 7 — RESTRAINED NODE C A R D S (IX,1 4 ,2X,3I l ,3F10.6)
One card for each restrained node.Total
of NVFIX cards (see Card Set 4).
C o l s . 2-5
NOFIX(IVFIX)
Restrained Node Number
8
Condition of restraint
IFPRE(IVFIXfI)
on displacement, w.
0 No restraint
1 node restrained
Condition of restraint
9
I F P R E (IVFIX,2)
on nodal rotation, ex .
0 No restraint
1 Node restrained
1 0
Condition of restraint
I F P R E (IVFIX,3)
on nodal rotation, © .
0 No restraint
1 node restrained
1 1 - 2 0
P R E S C (IVFIXfI)
The prescribed value of w.
21-30
P R E S C (IVFIX,2)
The prescribed value of e x .
31-40
P R E S C (IVFIX,3)
The prescribed value of e y .
NOTE:
If a subgrade is used it is not necessary to
prescribe any displacements.
CARD SET 8 — RIGID BODY C A R D S (215)-one card
Cols. 1-5 ' NRGD
Number of rigid bodies
6-10
NNDRGD
Total number of nodes
on all rigid bodies
C a r d SET 9— REFERENCE NODE C A R D S (I 5 )-One card for each
rigid body.
Cols. 1-5
REF(IRGD)
Reference node associated
with the rigid body.
CARD SET 10-MAXIMUM NO. NODES ON RIGID B O D Y (15)-one card
Cols. 1-5
MAXRGD
Maximum no. of nodes
on any rigid body.
53
CARD SET Il-RIGID BODY NODE C A R D S (14,8X,2013)-One card
for each rigid body.
Cols. 1-3
RGDND(IRGD,1)
1st node on rigid body
R G D N D (I R G D ,M A X R G D )
.last node on rigid
body
CARD SET 12-MATERIAL C A R D S (15,4F10.5)-One. card for each
different material.
Total of NMATS cards
(see Card Set 4).
Cols. 1-5
NUMAT
Material identification
number.
P R O P S (NUMATfI)
6-15
Elastic M o d u l u s , E=
16-25
P R O P S (NUMAT,2) ■ Poisson's R a t i o r v.
26-35
P R O P S (NUMAT,3)
Material Thickness, t.
36-45
P R O P S (NUMAT,4)
Distributed load, q.
CARD SET 13 -LOAD CASE TITLE CARD(18A4)-one card
Cols. 1-72
TITLE
Title of the load case
-limited to 72 characters
CARD SET 14 -LOAD CONTROL CARD(IS)-one card
Cols. 1-5
IPLOD
Applied point load
control parameter
O-No applied point loads
!-Applied point loads
to be input. .
CARD SET 15-APPLIED LOAD C A R D S (15,3F10.3)-one card
for each loaded nodal point.
LODPT
1-5
Node number
Load component in the
6-15
POINT(I)
z-direction.
Nodal couple in the
16-25
P O I N T (2)
xz plane.
26-35
Nodal couple in the
P O I N T (3)
yz plane.
NOTES: The last card should be that for the highest
numbered node whether it is loaded or not.
54
If IPLOD = O f omit this card set.
CARD SETS 13 TO 15 TO BE REPEATED FOR EACH LOAD CASE
IN ACCORDANCE WITH 'N C A S E 1 IN CARD SET 4.
CARD SETS 3 TO 15 TO BE REPEATED FOR EACH PROBLEM IN
ACCORDANCE WITH 'N P R O B ' IN CARD SET I.
Appendix B
Program listing
PROGRAM PLATE
C
C*** INPUT,OUTPUT,TAPE105»INPUT,TAPE108*OUTPUT,
C
TAPE I, TAPE Z, TAPE 3, TAPE 4
C
DIMENSION TITLE(IZ)
COMMONZLGOATAZCOORD(80,Z),PROPS(I0,4),PRESC(40,3),
*
ASOI S(Z40),EL0AD(Z4,Z4),NOT IX(40),
*
IFPRE(40,3),LNOOS(ZS,8),MATNO(Z5)
COMMONZWORXZELCOO(Z,8),SHAPE(8),DERIV(Z,8),DMATX(5,5),
*
CARTD(Z,8) ,DBMAT<5,Z4),BMATX(5,Z4) ,
*
SMATX( 5,24,9) ,POSGP(S) ,WE1GP(3),
»
GPC00(Z,9) ,NER0R(24)
commonzcontroZnpoin,nelem,nnooe,noofn,noime,
*
nstre,ntype,ngaus,nprop,nmats,
*
NVFIX,NEVA8,ICASE,NCASE,!TEMP,
*
IPR0B,NPR03
COMMONZWINXLRZ
*
IFNO,BMOOLS,TAREA,NDTYP,ENFLNC,
*
WINXMO(Z5),NOT YPE(80),EFSTIF(Z4,24),CPSTIF(24,24),
*
0EFMAT(8),ELDISP(Z4,8),NOFRC(Z4)
COMMONZRIGIOZ NRGD,MAXRGD,REF(5),RGONO(5,80),LNAOS(Z5,8)
OPEN (I,NAME*’*1',USAGE*'CREATE’>
OPEN (2,NAME»'‘Z’,USAGE-’CREATE’)
OPEN (3,NAME*'*3',USAGE«'CREATE’)
OPEN (4,NAME«'«4’,USAGE-’CREATE')
OPEN (5,NAME«’*5’,USAGE*’CREATE’>
OPEN (6,NAME*’*6*,USAGE*’CREATE’)
READ(105,900) NPROB
900 FORMAT(15)
WRITEd OS,905) NPROB
905 F0RMAT(1H0,5X.23HT0TAL ND. OF PROBLEMS «,I5)
DO ZO IPROB-I ,NPROB
READ (105,920) IFNO
920 FORMATE 15>
REWIND I
REWIND Z
REWIND 3
REWIND 4
REWIND 5
REWIND 6
READdO 5,910) TITLE
910 FORMAT(18A4)
WRI TE(108,915) IPROB,TITLE
915 FORMAT(ZZZZZ,6X,12HPR0BLEM NO. ,I3,10X,
•18A4)
IFdFND .NE.I) GO TO 930
WRITEd 08,925)
925 FORMAT (1XZlX,’‘‘LUMPED WINXLER FOUNDATION“ ’)
GO TO 940
930 IF(IFND.NE.Z) GO TO 940
WRITEd 08,935)
935 FORMATI 1XZlX,’“ INTEGRATED WINXLER FOUNDATION**' >
940 CONTINUE
C
C “ CALL THE SUBROUTINE WHICH READS MOST OF THE DATA
C
CALL INPUT
C
C “ CREATE THE ELEMENT STIFFNESS FILE
56
c
CALL STIFPB
OO 10 ICASE«1 .NCASE
C
C*** COMPUTE LOADS, AFTER READING THE RELEVANT
C
EXTRA DATA
C
CALL LOAOPB
C
C *« MERGE AND SOLVE THE RESULTING EQUATIONS
C
BY THE FRONTAL SOLVER
C
CALL FRONT
C
C
COMPUTE THE STRESSES IN ALL THE ELEMENTS.
C
CALL STREPS
CALL FPRES
10 CONTINUE
20 CONTINUE
STOP
END
SUBROUTINE INPUT
C
C*** READ THE FIRST DATA CARD, AND ECHO IT
C
IMMEDIATELY,
C
COMMON/LGDATA/COOR0(80,2),PROPSC10,AI,PRESCK 0,3),
*
ASOI SC240),EL0AD(2A,20,NOFIXUO ),
*
IFPRE(40,3)»LNODS(25#8),MATNOC25)
COMMON/WORK/ELCOD(2,8),SHAPE(8),DERIV(2,8),DMATXC5,5),
»
CARTDC2,8),DBMAT CS,24),BMATXC5,24),
«
SMATX C5,24,9),P0SGPC3),UEIGPC3),
»
GPCODC2,9),NER0RC24)
COMMON/CONTRO/NPOIN,NELEM,NNODE,NOOFN,NDIME,
*
NSTRE,NTYPE,NGAUS,NPROP,NMATS,
*
NVFIX,NEVAB,!CASE,NCASE,!TEMP,
*
IPROB,NPROB
COMMON/WINKLR/
*
ifno,bmodls,tarea,ndtyp,enflnc,
*
WINKMDC25),NDTYPE C80),EFSTIF(24,24),CPSTIFC24,24),
*
9EFMATC8),EL0ISP(24,8),NDFRC(24)
COMMON/RIGID/ NRGD,MAXRGD,REF(5),RG0NDC5,80),LNADS(25,8)
READC105,900) NPOIN,NELEM,NVFIX,NCAS£,NTYPE,
*NNODE,NDOFN,NMATS,NPROP,NGAUS»NDIME,NSTRE
800 FORMATC10I5,F10.5>
900 FORMAT C1215)
NEVAB*NDOFN»NNOOE
WRITE(I08,905) NPOIN,NELEM,NVFIX,NCASE,NTYPE,
*NNODE,NDOFN,NMATS,NPROP,NGAUS,NDIME,
•NSTRE,NEVAB
905 FORMAT(Z/8H NPOIN »,I4,4X,8H NELEM «,I4,
* 4X,8H NVFIX *,14,4X,BH NCASE *,I4,4X,
* RH NTYPE *#I4,4X,SM NNODE
* RH NDOFN 14// 8H NMATS
4,4X,
* RH NPROP I4,4X,8H NGAUS *zI4#4X#
* RH NDIME ■/I4,4X,Bh NSTRE *#I4#4X/
* RH NEVAq 14)
CALL CHECKI
C
C*** ZERO ALL THE NODAL COORDINATES
C
IT IS NECESSARY TO READ IN ALL NODE
57
C
C
C O O R D I N A T E S FOR A L U M P E D F O U N D A T I O N
DO ?n I PO IN-I , NPOI N
DO 20 I D I M E - 1 , ND IME
20 C O O R D I I PO I N , ! D I M E ) -0.0
DO 21 I E L E M - 1 , N E L E M
21 W I N K M D I I E L E M ) » 0 . 0
C
C •*• R EAD THE E L E M E N T N O D A L C O N N E C T I O N S , AND
C
THE P R O P E R T Y N U M B E R S ,
C
IFI I F N O . E Q , O ) G O TO 1 70
WRI TE(I OS,810)
810 F 0 R M A T I / / 8 H E L E M E N T , 3 X , 8 H P R O P E R T Y , 1 8 X , 1 2 H N O D E N U M B E R S
* , I6 X , I 2H SOI L M O DU L U S )
DO I 10 I E L E M - 1 , N E L E M
R EA D 11 05 , 8 0 0 ) N U M E L , M A T N O ( N U M E L ) ,
* I L N O D S I N U M E L ,1 N O D E ) ,I N O D E - 1 , N M O O E ),W I N K M O I N U M E L )
110 WRI TE 11 O S ,815) N U M E L , M A T N O I N U M E L ) ,
• I L N O D S I N U M E L , ! N O D E ) , I N O O E - I , N N O O E ),W I N K M O t N U M E L )
8 1 S F O R MAT I I X , 1 5 , 1 9 , 6 X , 8 1 5 , 5X, F 10.5)
IFI I FN 0 . E D . 2 ) GO TO 115
C
C -*- READ N ODAL P O I N T C O O R D I N A T E S AND F O U N D A T I O N M O D U L U S
C
WRI T E H 08,820)
820 F O R M A T I / / 2 5 H
N O D A L POINT C O O R O I NA TE S , 6 X ,9 H N O D E T Y P E )
U R I T E I 1 0 8 ,8 2 5)
825 F O R M A T I 6 H N 0 0 E , 7 X , 1 H X , 9 X , 1 H Y >
130 R E A O t I O 5,830) I P O I N , I C O O R D I IPOIN,I DI M E ),
• IO I M E - I , NOI M E ) , NO TYPE IIPO IN)
I F I I P O I N . N E . N P O I N) G O TO I 30
830 F OR MAT I 1 5 , 2 F 1 0 . 5 , 1 5)
DO I 50 I P O I N - 1 , N P O I N
150 W R IT E I1 0 8 ,8 3 5) I PO I N , I C O O R D t I PO I N , ! D IM E) ,
* I 0 1 M E - 1 , N O I M E ) , N O T Y P E IIP OIN )
835 F O R M A T ( 1 X , I 5 , 2 F 1 0 . 3 , 5 X , I 5 )
GO TO I 90
170 W R I T E I 1 0 8 , 9 1 0 )
910 F O RM A T ( //BH E L E M E N T , 3 X , 8 H P R 0 P E R T Y , 6 X ,
* 12HN00E N U M B E R S )
DO 10 I E L E M - I , N E L E M
R E A D ( 10 5, 90 0) N U M E L , M A T N O I NUM EL ) ,
• I L N O O S ( N U M E L , I N O D E ) , IN O D E - I , N N O D E )
10 W R I T E ( 1 0 8 , 9 1 5 ) N U M E L , M A T N O I N U M E L ) ,
- IL NOD S ( N U M E L , I N O D E ) , I N O D E - 1 ,N N O D E )
915 F O R M A T ( 1 X , I 5 , I 9 , 6 X , 8 I 5 )
C
C -** R EAD S OM E N O D AL C O O R D I N A T E S , F IN I SH I NG
C
W IT H THE L A S T N O D E OF ALL.
C
115 C O N T I N U E
W R I T E O 08, 920 )
920 F O RM A T I 7 / 25 H
N O D A L POINT C O O R D I N A T E S )
WRI TE(I 0 8 ,9 25 )
925 F O R M A T I6H
N00E,7X,1HX,9X,1HV)
30 R E A O ( 1 0 S , 9 3 0 > I PO I N , I C OO RO I IP O I N,I D I M E ),
• IDIME»1,NDIME>
930 F O RM A T I 1 5 , 5 F 1 0 . 5 )
I F I I POl N. NE. NPOI N) GO TO 30
C
C--
I N T E R P O L A T E C O O R D I N A T E S OF M I D S I D E N ODES
58
If(ND1ME. EQ.1) GO TO 40
CALL NODEXY
40 CONTINUE
DO 50 IPOIN«1,NPOlN
50 URITE(I09,935) IPOIN,(COORDU POIN,!DIME),
* IDIME»1,NDIME)
935 F0RMAT<1X,I5,3F10.3)
190 C O N T I N U E
IF(NVFIX.Ea.O)
GO TO 9 0
C
C*** READ THE FIXED VALUES,
C
URITE(IOS,940)
940 F0RMAT<//17H RESTRAINED NODES)
WRlTE(I 08,945)
945 FORMAT (5H N0DE,ZX,4HC00E,10X,
'IZHFIXED VALUES)
IF(NDOFN.NE.Z)GO TO 70
DO 60 IVFIX»1,NVF IX
READ (105,950) NOFIX(IVFIX) ,(!FPRE(IVFIX,
* ID0FN),ID0FN»1,ND0FN),(PRESC(IVFIX,ID0FN),
» IOOFN»1,NOOFN)
60 URITE(I 08,950) NOFIX(IVFIX),(IFPRE(IVFIX,
* IDOFN),IDOFN*1,NDOFN),(PRESC(1VFIX,IDOFN),
* IOOFN»1,NDOFN)
950 FORMAT!IX,14,3X,ZII,ZF10.6)
GO TO 90
70 DO 80 IVFIX*1,NVFIX
READ (105,955) NOFIX(IVFIX) ,(IFPREdVF IX,
* ioofn),ioofn«i,noofn),(presc(ivfix,
* IDOFN),1DOFN-I,NDOFN)
80 URITE(108,955> NOF IX(IVFIX),(IFPRE (IVFIX,
* IDOFN),IDOFN=I,NDOFN),(PRESC(IVFIX,
* IDOFN),I DOFN=I,NDOFN)
955 FORMAT(IX,I4,ZX,31 1.3F10.6)
90 CONTINUE
READ(105,700) NRGO ,NNORGO
700 FORMAT (215)
URI TE(I08,710) NRGD,NNDRGD
710 FORMAT(//Z6H NUMBER OF RIGID BODIES »,I3,/
» 35H NUMBER OF NODES ON RIGID BODIES =,I3)
IF(NRGD.EQ.O) GO TO 240
WRI TE(I 08,720)
720 FORMAT!//37H RIGID BODY NUMBER
REFERENCE NODE)
DO 210 IRGD=I,NRGD
READ(105,730> REF(IRGD)
ZIO WRITE(108,740) IRGD,REF(IRGD)
730 FORMAT (15)
740 FORMAT (IX,10X,1 3,1 7X,I3)
READ(105» 750) MAXRGD
750 FORMAT(IS>
WRITEd 08,760) MAXRGD
760 FORMAT(ZZ43H MAXIMUM NUMBER OF NODES ON A RIGID BODY =,I3)
DO ZZO IRGD=I,NRGD
ZZO READ(105,770) (RGDND(IRGD,NODE),NODE=I,MAXRGD)
770 FORMAT (2413)
WRITEO 08,780)
780 FORMAT(/23H RIGID BODY
NODES)
DO 230 IRGO=I,NRGO
230 WRITE(I 08,790) IRGD,(RGDND(IRGD,NODE),NODE=I,MAXRGD)
790 FORMAT(14,ax,ZOI3)
59
240 CONTINUE
C
C**« READ THE AVAILABLE SELECTION O f ELEMENT
C
PROPERTIES,
C
WRITEO 08,960)
960 FORMAT(//21H MATERIAL PROPERTIES)
WRlTEO 08,965)
965 FORMAT(BH NUMBER,6X,I4HY0UN6S MODULUS,ZX,
* 15HP01SSON1S RATIO,ZX,9HTHICXNESS,2X,
* 1ZHUNI FORM LOAD)
DO TOO IMATS-I,NMATS
READ (105,930) NUMAT,(PROPSINUMAT,! PROP),
* IPROP-T,NPROP)
TOO WRITE(I 08,970) NUMAT,IPROPSINUMAT,IPROP),
* IPR0P»1,NPR0P>
970 FORMAT IIX,15,7X,5E14.6)
C
C*** SET UP GAUSSIAN INTEGRATION CONSTANTS
C
CALL GAUSSO
CALL CHECKZ
RETURN
END
SUBROUTINE NODEXY
C
C••• LOOP OVER EACH ELEMENT
C
COMMON/LGOATAZCOORDI80,Z),PROPS110,4),PRESC140,3),
*
ASDISI240),EL0ADI24,24),N0FIXI40),
*
IFPREI40,3),LN00SIZ5,8),MATN0IZ5)
COMMON/WORK/ELCOOtZ,8),SHAPEI8),OERlVIZ,8),DMATXl5,5),
*
CARTDIZ,8),DBMATI5,Z4),BMATXI5,Z4),
*
SMATXI5,24,9),POSGP13),WEIGP13),
*
GPC0DI2,9),NER0RIZ4)
COMMON/CONTRO/NPOIN,NELEM,NNOOE,NOOFN,ND1ME,
»
NSTRE,NTYPE,NGAUS,NPROP,NMATS,
*
NVFIX,NEVAB,!CASE,NCASE,!TEMP,
*
IPROB,NPROB
COMMON/WINKLRZ
*
IFNO,BMODLS,TAREA,NOTYP,ENFLNC,
*
WINKMDIZ5),NDTYPEI80),EFSTIFIZ4,Z4),CPST1FIZ4,24),
*
BEFMAT18),ELDISPI24,8),NDFRC124)
DO 30 IELEM-1,NELEM
C
C--- LOOP OVER EACH ELEMENT EDGE
C
DO ZO IN0DE-1,NN0DE,Z
C
C--- COMPUTE THE NODE NUMBER OF THE FIRST NODE
C
NOOST-L NO DS(IELEMfINOOE)
IGASH-INODE-Z
iFiigash.gt.nnode) igash-1
C--- COMPUTE THE NODE NUMBER OF THE LAST NODE
C
C
NOOFN-L NO DSIIELEMfIGASH)
MIDPT-INOOE-I
C
C-** COMPUTE THE NODE NUMBER OF THE INTERMEDIATE NODE
C
60
NODMOHi NOOS(I ElEMtMl OPT)
TOTAL«ABS(COOROINOOMDtI))*
C
* ABS(COORD(NODMO/2))
C*** JF THE COOORDINATES OF THE INTERMEDIATE
C
NODE ARE BOTH ZEROt INTERPOLATE BY A
C
STRAIGHT LINE.
C
IF(TOTAL.GT.O.O) GO TO 20
KOUNT *1
10 COORDfNODMDtKOUNT)s(£OORO(NODSTtKOUNT)*
* COORDfNO OFNtKOUNT))/2.O
K0UNT»K0UNT*1
IF(K0UNT.E0.2> GO TO 10
20 CONTINUE
30 CONTINUE
RETURN
END
SUBROUTINE GAUSSO
COMMON/LGDATAZCOOROf80t2)tPROPS(10tA)tPRESC(40t3)t
*
ASOI Sf240)tELOAD(24t2A)t NOF IXfAO)t
*
I FPRE(AOtl)tLNOOS(25t8)tMATNOf25)
COMMON/UORK/ELCOD(2t8),SHAPE(8)tOERIV(2t8)tDMATX(5t5)t
*
CARTOf2,8)tOBMAT(5t2A)tBMATX(5t2A)t
*
SMATX(5t2A,9),POSGP(3)tUEIGP(3)t
*
GPC0D(2t9)tNER0R(24)
COMMON/CONTRO/NPOIN,NELEMtNNODEtNDOFNtNDIMEt
*
NSTREt NT YPEtNGAUSt NP ROPtNMATSt
*
NVFIXtNEVABtICASEtNCASEtITEMP,
*
IPROBtNPROB
COMMON/UINKLR/
*
IFNDtBMODLStTAREAtNDTYPtENFLNCt
*
UINKMD(25),NOTYPE(80)tEFSTIF(24,24),CPSTIF(24,24),
*
BEFMAT(S),ELDISP(24,8),NDFRC(24)
I F(NGAUS.GT.2) GO TO 10
POSGPd >»-0.577350269189626
WEIGPd )»1.0
GO TO 20
10 POSGPd )»-0.774596669241483
P0SGP(2)»0.0
POSGP(3>»-POSGP(I)
WEIGPd )«0.555555555555556
WEIGP(2)»0.888888888888889
WEIGP(3)»WEIGP(1>
GO TO 40
20 KGAUS«NGAUS/2
DO 30 IGASH=I,KGAUS
JGASH=NGAUS*!-IGASH
POSGPfJ GASH)=-POSGP(IGASH)
WEIGP(JGASH)=WEIGPd GASH)
30 CONTINUE
40 CONTINUE
RETURN
END
SUBROUTINE STIFPB
C
C*»* CALCULATES ELEMENT STIFFNESS MATRIX
C
FOR PLATE BENDING ELEMENT
C
COMMONZLGDATAZCOORD(80,2),PROPS(10,4),PRESC(40,3)t
*
AS0IS(240),EL0AD(24,24),N0FIX(40),
*
IFPRE(40,3),LN0DS(25,8),MATN0(25)
61
COHMONZUORK/ELCOO(2,8),SHAPE(8),OERIV(2,8),I>M*TX(S,5),
•
CARrD(2,8),D8MAT(5/24),BMATX(5»24>,
•
SMATX(5,2*,9),POSGP(3)#WEIGP<3)»
•
GPC0D(2,9),NER0R(24)
COHMON/CONTROZNPOIN,NELE,
1,NNODE/NOOFN,NDIME,
•
NSTRE»NTVPE,NGAUS/NPROP,NMATS,
«
NVEIX,NEVA8/ICASE»NCASE/ITEMP»
«
IPROB/NPROB
COMMONZWINKLR Z
‘
IEND#8M0DL S#TAREA/NOTYP#ENFLNC #
•
WINKMD(25),NOTYPE(80)»EFSTIF(24,24),CPSTIF(24,24),
«
BEFMAT(8),ELDISP(24,8),NOFRC(24)
DIMENSION ESTIF(24,24)
C
C*** LOOP OVER EACH ELEMENT
C
DO 70 IELEM*1,NELEM
LPROPeMATNO(IELEM)
IF(IFND.LT.I) GO TO 15
BMODLSeWINKMD (IELEM)
15 CONTINUE
C
Ceee EVALUATE THE COORDINATES OF
C
THE ELEMENT NODAL POINTS
C
DO 10 INODEeI,NNODE
LNODEeLNODS(IELEM,INODE)
DO 10 IDIME»1 ,NDIME
ELCOD(IDIME, INODE)eCOORD(LNODE,IDIME)
10 CONTINUE
C
c*** initialize the element stiffness matrix
c
DO 20 IEVABeI,NEVAB
DO 20 JEVABeI,NEVAB
ESTIF (IEVAB,JEVAB) eOeO
IF(IFNDeLTeI) GO TO 20
EFSTIF(IEVAB,JEVAB)e0.0
CPSTIF( IEVAB,JEVAB)eOeO
20 CONTINUE
TAREAeOeO
C
C ee calculate matrix of elastic rigidities
C
CALL MODPBILPROP)
KGASPeO
C
Ceee ENTER LOOPS FOR NUMERICAL INTEGRATION
C
DO 50 IGAUSeI,NGAUS
EXISP-POSGP(IGAUS)
DO 50 JGAUS-I,NGAU S
ETASP-POSGPUGAUS)
KGASP-KGASP*1
C
C e evaluate the shape functions.
C
ELEMENTAL AREA,ETC.
C
CALL SFR2(EXISP.ETASP)
CALL JAC0B2(IELEM,DJACB,KGASP)
DAREA-DJACB'WEIGP(IGAUS)-WE IGP(JGAUS)
TAREA-TAREA-DAREA
62
c
C»»* EVALUATE THE B AND DB MATRICES
C
CALL BMATPB
CALL DBE
C
C
CALCULATE THE ELEMENT STIFFNESS
C
DO 30 IEVAB-I ,NEVAB
DO 30 JEVAB*IEVAB*NEVAB
DO 30 ISTREaIsNSTRE
ESTIFU EVABsJEVABIaESHFUE VABsJEVAB>♦
•BMATX(ISTREsIEVABI‘DBMAT(ISTREsJEVASI
••DAREA
30 CONTINUE
C
Caaa CALCULATE THE INTEGRATED HINKLER
C
STIFFNESS MATRIX IF REQUIRED
C
IF(IFND.NE.21 GO TO 37
DO 35 INODEaIsNNODE
Ia3*INODE-2
DO 35 JNODE*INODEs NNODE
Ja3*JNODE-2
35 EFSTIF(IsJ)«SHAPE(INODEl*SHAREUNO DElaDAREA
••BMOOLS+EFSTI FUsJI
37 CONTINUE
C
Ca* STORE THE COMPONANTS OF THE DB MATRIX
C
FOR THE ELEMENT
C
DO 40 ISTREaIsNSTRE
DO 40 IEVAB»1sNEVAB
SMATXU STREsIEVABsKGASP1»
*DSMAT(ISTREsIEVABl
40 CONTINUE
SO CONTINUE
C
Caaa CONSTRUCT THE LOWER TRIANGLE OF THE
C
ELEMENT AND FOUNDATION STIFFNESS MATRACIES
C
DO 60 IEVABaTsNEVAB
DO 60 JEVAB»T,NEVAB
ESTIFU EVABsIEVABl=ESTIFUEVABsJEVABI
IF(IFND.NE.21 GO TO 60
EFSTIF HE VABsIEVABI=EFSTIFUE VABsJEVABI
60 CONTINUE
IFUFND.LT. Tl GO TO 67
IFUFNO.GT.il GO TO 65
DO 63 INODE«lsNNODE
LNODE'LNODSUELEM, INODE)
NOTYP=NDTrPE<LNODEI
IF(NDTYP.EQ.II ENFLNC*!.0/12.0; GO TO 63
IF(NDTYP.EQ.21 ENFLNC a l . 0/6.O
63 EFSTIFI3«IN0DE-2s3a|NODE-21 =BMODLS*TAREA*ENFLNC
65 DO 66 IEVAB=T,NEVAB
DO 66 JEVAB=TsNEVAB
66 CPSTlF UE VABsJEVAB I=ESTIF U EVABsJEVABlaEFSTI FUEV ABsJEVASI
WRITEISl EFSTIF
WRITE 161 CPSTIF
67 CONTINUE
63
C••• STORE THE STIFFNESS MATRIX,STRESS MATRIX
C
AND SAMPLING POINT COORDINATES FOR
C
EACH ELEMENT ON DISK FILE
HRITE(I) ESTIF
URITE(S) SMATX,GPCOD
70 CONTINUE
RETURN
END
SUBROUTINE MOOPB(LPROP)
C
C‘*» CALCULATES MATRIX OF ELASTIC RIGIDITIES
C
FOR PLATE BENDING ELEMENT
C
COMMON/LGOATA/COORO(80,2>,PROPS(10,4),PRESC(40,3),
*
ASDIS(240),EL0AD(24/2C),NOFIX(AQ)/
*
IFPRE(AO,3),LNOOS(25,8),MATNO(25)
COMMON/WORK/ELCOD(2,8),SHAPE(8),OERIV(2,8),DMATX(5,5),
*
CARTD(2,8),DBMAT (5,24),BMATX(5,24),
*
SMATX<5,24,9),POSGP(3),UEIGP(3),
*
GPCOO(2,9),NEROR(24)
commonzcontro/npoin,nelem,nnode,ndofn,noime,
*
nstre,ntype,ngaus,nprop/Nmats»
*
nvfix,nevab,icase,ncase,itemp,
*
IPROB,NPROB
COMMON/WINKLR/
*
IFND,BMODLS,TAREA,NDTYP,ENFLNC,
*
UINKMO(25),NOTYPE (80),EFSTIF(24,24 ),CPSTIF(24,24),
*
BEFMAT(S),ELDISPl24,8),NDFRC(24)
DO 10 ISTRE»1,NSTRE
DO 10 JSTRE-I,NSTRE
OMATX(ISTRE,JSTRE)«0.0
10 CONTINUE
YOUNG-PROPS(LPROP, I)
POlSS»PR0PS(LPR0P,2)
THICK-PROPSILPROP,3)
DMATXd ,1)-YOUNG-I THICK--3)
*/(12.0* (1.O-POI SS**2))
DMATX(2,2I-DMATX(1,1)
DMATXd /2)*P0ISS*DMATX (1,1 )
0MATX(2,1I-DMATX(1,2)
DMATX(3,3)»(1.0-P0ISS)*0MATX(1,1)/2.0
DMATX (4,4I-YOUNG‘THICK/<2.4* (I.OtPOISS) )
OMATXIS,SI-DMATX(4,4)
RETURN
END
SUBROUTINE SFR2 (S,T)
C
C*** CALCULATES SHAPE FUNCTIONS AND THEIR
C
DERIVATIVES FOR 2D ELEMENTS
C
COMMONZLG DATA/COORDl80,2),PROPS(I0,4),PRESC(40,3),
*
ASD1S(240)»EL0A0(24,24),N0FIX(40),
*
IFPRE(40,3),LNODS(25,8),MATNO(25)
C0MM0N/W0RK/ELC0D(2,8),SHAPE(8),0ERIV(2,8),DMATX(5,5),
*
CART D(2,8),DBMAT(5,24),BMATX(5,24),
*
SMATX(5,24,9),POSGP(3),UEIGPl3),
*
GPC0D(2,9),NER0R(24)
COMMON/CONTROZNPOIN,NELEM,NN00E,ND0FN,NDIME,
*
NSTRE/NT YPE/NGAUS/NPROP/NMATS,
*
NVFIX,NEVAB, ICASE/NCASE,ITEMP,
*
IPROB,NPROB
COMMON/UINKLRZ
64
C
C
C
*
IFNO,BMOOlS,TARE*,NOTrP,ENHNC,
*
UINKM0(25),NDTVPE (80),EFSTIF(24,2*>.CPSTlF(2t,2A),
«
BEFMAT(8),EUOISP(24,8),NOFRC(24)
S2»S«2.0
T2 *T*2 ,O
SS*S*S
TT*T*T
ST■S*T
SST«S**2«T
STT«S*T**2
ST2«S*T*2.0
SHAPE FUNCTIONS
SHAPE<1>«(-1.0»ST+SS*TT-SST-STT)/4.0
SHAPE<2)*(I.O-T-SSTSST)Z2.O
SHAPE(3)»(-1.O-STTSStTT-SST*STT)/4.O
SHAPE(4)s(I.OtS-TT-STT)/2.O
SHAPE(S)«(-1.OTSTTSSTTTTSSTTSTT)/4.O
SHAPE(6)»(I.OtT-SS-SST)/2.O
SHAPE<7>«<-1.0-STtSStTTtSST-STT)/4.O
SHAPE<8)»<1.O-S-TTTSTT)/2.O
C
Cttt SHAPE FUNCTION DERIVATIVES
C
OERIVd ,1)=(TtSZ-STZ-TT)/4.O
OERIVd ,2)»-STST
0ERIV(1,3)»(-Tts2-ST2tTT)/4.0
OERIVd ,4)«(1.O-TT)/2.0
DERIV(1,5)*(TtS2tsT2ttT)/4.0
OERIVd ,6)i-S-ST
DERIVC1,7)«(-TtS2tST2-TT>/4.0
OERIVd ,8)«(-1.0tTT>/2.0
DERIV(2,1)«(StT2-SS-ST2>/4.0
DERIV(2,2)«(-1.0tSS)/2.0
0ERIV(2,3)«(-StT2-SStST2)/4.0
0ERIV(2,4)»-T-ST
0ERIV(2,5)«(StT2tSStST2)/4.0
0ERIV(2,6)«(1.O-SS)/2.O
0ERIV(2,7)»(-STT2tSS-ST2)/4.0
0ERlV(2,8)»-TtST
RETURN
END
SUBROUT INE JACOB2( IELEM,D/ACB,KGASP)
C
C*** CALCULATES COORDINATES OF GAUSS POINTS
C ANO THE JACOBIAN MATRIX AND ITS DETERMINANT
C ANO THE INVERSE FOR 20 ELEMENTS
C
DIMENSION XJACM(2,2),XJACI(2,2)
COMMON/LGDATA/COOR0(80,2),PROPS(10,4),PRESC(40,3),
T
ASD1S(240),ELOAO(24,24),NOFIX(40),
•
IFPRE(40,3),LNOOS(25,8),MA1NO(25)
COMMON/UORK/ELCOO(2,8),SHAPE(8),DERIV(2,8),OMATX(5,S),
t
CARTO(2,8),OBMAT(5,24),BMATX(5,24),
•
SMATX(5,24,9),POSGP(3),UEIGP(3),
•
GPCOD (2,9),NEROR (24)
COMMON/CONTRO/NPOIN,NELEM,NNOOE,NOOFN,NHIME,
*
NSTRE,NTVPE,NGAUS,NPROP»NMATS,
*
NVFIX,NEVAB,!CASE,NCASE,!TEMP,
*
IPROB,NPROB
COMMON/UINKLR/
65
*
*
*
IFND,BMOOLS.TARE*,NOrVP,ENFLNC<.
UINKH0(?5),NDTYPE(80),EFSTIF<24»2*)»CPST1F(ZA,2A),
BEFMAT(8)?EL0ISP(24/8)/NDFRC(24)
C
C*** calculate coordinates of sampling point
C
DO IO IDIME-1,NO IME
GPCODd DIME,KGASP) «0.0
DO 10 IN0DE«1,NNODE
GPCOD(IDIME,KGASP)-GPCOD(!DIME,KGASP)*
* ELCOOI IDIME,INODE )*SHAPE(INODE)
10 CONTINUE
C
C*** CREATE JACOBIAN MATRIX, XJACM
C
DO 20 IDIME=I,NOIME
DO 20 J0IME«1,NOIME
XJACM (IOIME,JDIME)=0.0
DO 20 INOOE=I ,NNOOE
XJACMIIDI ME,JDIME)«XJACM(IDIME,JDIME)*
* DERIVI IDIME,INODE)*ELCOD IJDlME,INODE)
20 CONTINUE
C
C«*• CALCULATE DETERMINANT AND INVERSE OF
C
JACOBIAN MATRIX
C
DJACB=XJACM(1,1)*XJACM(2,2)-XJACM(1,2)*
* XJACM(2»1>
IFIDJACB.GT.O.O) GO TO 50
URITE(1 08,900> IELEM
STOP
30 XJACIII,1)»XJACM(2,2)/DJACB
XJACI<2,2)=XJACM11,1)/DJAC8
XJACI (I,2)— XJACM11,2)/DJACB
XJACI(2,1)»-XJACMI2,I)/DJACB
C
C * CALCULATE THE CARTESIAN DERIVATIVES
C
DO 40 IDIME=I,NDIME
DO 40 INOOE=I,NNODE
CARTDIIOI ME,INODE)»0.0
DO 40 JDIME=I,NOIME
CARTDI IDIME,INODE)=CARTDl IOIME,INODE)♦
* XJACI (!DIME,JDIME )*DERIVIJDIME,INODE)
40 CONTINUE
900 FORMAT!//,IX,24HPROGRAM HALTED IN JAC0B2,
* /,11X,22H ZERO OR NEGATIVE AREA,/,
* 10X,16H ELEMENT NUMBER ,15)
RETURN
END
SUBROUTINE BMATPB
C
C*«« CALCULATES STRAIN MATRIX 9
C
FOR PLATE BENDING ELEMENT
C
COMMON/LGDATA/COOROI80,2),PROPSII0,4),PRESC I40,3),
*
AS0IS(240),EL0AD(24,24),N0FIX(40),
*
IFPRE(40,3),LN0DS(25,8),MATN0(25)
C0MM0N/U0RK/ELC0D(2,8),SHAPE(8),DERIV(2,8>,DMATX(5,5>,
«
CARTDI2,8),DBMAT I5,24),BMATX(5,24),
*
SMATXI5,24,9),P0SGPI3),WEIGPI3),
*
GPC0D(2,9) ,NERORI24)
66
COMMON/CONTRO/NP01N,NELEM,NNODE,NDOFN,NDIME,
*
NSIRE,NTVPE,NG*US,NPROP,NM*TS,
*
NVFIX,NEVA8,ICASE,NCASE,!TEMP,
*
IPROBfNPROB
COMMON/WINKLR/
*
IFNB,BMODLS,TAREA,NOTTP,ENFLNC,
*
UlNKMD(25),NOTYPE (80),EFSTIF(ZA,2*),CPSTI F<24,20,
*
9EFMAT(8),ELOISP(2A,8),NOFRC(2A)
DO 10 ISTRE»1,NSTRE
DO 10 IEVAB»1 ,NEVAB
10 BMATX(ISTRE,IEVAB)-0.0
JGASH=O
DO 20 INODE=I,NNODE
IGASH=J GASHtI
BMATX(A,IGASH)=CARTO(I,INODE)
BMATX (SfIGASH)=CAR TO(2,INODE)
IGASH=IGASHtI
JGASH=IGASHtI
BMATX(IfIGASH)=-CART0(1,INODE)
BMATX(3,IGASH)*-CARTD(2,1NODE)
BMATX(A,IGASH)=-SHAPE(INOOE)
BMATX <2,JGASH)=-CARTO(2,1NOBE)
BMATX(3,JGASHj=-CART0(1,INODE)
BMATX(SfJGASH)=-SHAPE(INODE)
20 CONTINUE
RETURN
END
SUBROUTINE DBE
C
Cttt CALCULATES D*8
C
COMMON/LGDATA/COORO(80,2),PROPS<10,A),PRESC(AO,3),
t
ASDIS(2A0),EL0A0(2A,ZA),NOFIX(AO),
*
IFPRE(AO,3),LNOOS(25,8),MATNO(25)
COMMON/WORKZELCOD(2,8),SHAPE(8),DERIV(2,8),DMATX(5,S),
*
CARTD(2,8),DBMAT(5,2A),BMATX(5,2A),
*
SMATX(5,24,9),POSGP(3),WEIGP(3),
*
GPCOD(2,9),NEROR(ZA)
COMMONZCONTRO/NPOIN,NELEM,NNODE,NDOFN,NDIMEf
*
NSTRE,NTYPE,NGAUS,NPROP,NMATS.
*
nvfix,nevab,icase.ncase,itemp,
»
IPROBfNPROB
COMMONZWINKLRZ
«
IFND,BMODLS,TAREA,NDTYPfENFLNC,
*
WINKMD(25),NDTYPE(80),EFSTIF(24,2A),CPSTIF(24,24),
*
BEFMAT(8).ELDISP(2A,8),NDFRC(ZA)
DO 10 ISTRE=I,NSTRE
DO 10 IEVAB=I,NEVAB
DBMAT(ISTREfIEVAB)=0.0
DO 10 JSTRE=I ,NSTRE
DBMAT(ISTREfIEVAB) =DBMATdSTREfIEVAB)t
=DMATXd STRE,JSTRE) *BMATX(JSTRE,IEVAB)
10 CONTINUE
RETURN
END
SUBROUTINE LOAOPB
C
C»*t CALCULATE NODAL FORCES FOR PLATE ELEMENT
C
DIMENSION TITLE(12),POINT(3)
COMMONZLGDATAZCOORD(80,2),PROPS(10,A),PRESC(AO,3),
*
ASDIS(ZAO).EL0AD(2A,24),NOFIX(AO),
67
*
IFPRE(40,3)»LNODS(25,8),MATNO(ZS)
COMMON/UORK/ELC0D(2,8),SHAPE(S),DERIV(Z,8),DMATX(S,S),
*
CARTD(2,8),0BMAT(5,24),8MATX(5,24),
*
SMATX(5,ZA,9),POSGP(J),HEIGP(J),
*
GPCOO(2,9),NEROR(ZA)
COMMON/CONTRO/NPOIN,NELEM,NNOOE,NOOFN,NBIME,
*
NSTRE,NT YPE,NGAUS,NPROP,NMATS,
*
NVFIX,NEVAB,!CASE,NCASE,ITEMP,
*
IPROB,NPROB
COMMON/WINXLR/
*
IFN0,8M0DLS,TAREA,N0TTP,ENFLNC,
*
WINXMO(ZS),NOTVPE(80),EFSTIF(24,24>,CPSTIF(24,24),
»
BEFMAT(S),EL0ISPC24,8),NOFRC(24)
OO 10 IELEM-I ,NELEM
00 10 IEVAB=I,NEVAB
ELOADd ELEM,IEVA8)«0.0
10 CONTINUE
READOO 5,900) TITLE
900 FORMAT(18A4)
HRITE(I08,905) TITLE,ICASE
90S FORMAT (1X/1X,18A4, 5X,1 2H LOAD CASE «,I3)
C
C««» READ DATA CONTROLLING LOADING
C
TYPES TO BE INPUT
C
READ(105,910) IPLOO
910 FORMAT!IS)
WRI TE(108,915> IPLOD
915 FORMAT(IS)
GO TO 60
C
C»*• READ NODAL POINT LOADS
C
15 CONTINUE
1 F(1PLOO.EO.O) GO TO 115
20 READ( 105,920)
"LODPT,(POINT(IDOFN),IDOFN'1,NDOFN)
WRITEd 08,925)
«100PT,(POINT(IDOFN),IDOFN'1,NDOFN)
920 FORMAT!I5.3F10.5)
925 FORMAT(I5,3F10.5)
C
C
ASSOCIATE THE NODAL POINT LOADS
C
WITH AN ELEMENT
C
DO 30 IELEM*1.NELEM
DO 30 INODE=I,NNODE
NLOCA=LNODS(IELEM,INODE)
IFUODP T.EQ.NLOCA) GO TO 40
30 CONTINUE
40 DO 50 IDOFN=I,NDOFN
NGASH=(INODE-I)=NDOFN»IDOFN
eload(ielem,ngash)=point(ioofn)«eload(ielem,ngash)
50 CONTINUE
IF(LODPT.NE.NPOIN) GO TO 20
GO TO 115
60 CONTINUE
C
C*«« LOOP OVER each element
C
DO 110 IELEM=I,NELEM
LPROP=MATNO(IELEM)
68
UDLOD«PROPS(LPROP,A)
If(UOLOO.EQ.O.O) GO TO 110
C
C*** EVALUATE THE COORDINATES OF THE
C
ELEMENT NODAL POINTS
C
DO 70 IN0DE»1,NNOOE
LNODE-LNODSCIELEM, INODE)
DO 70 IDIME-1,NOIME
ELCOOC IDIME,INODE)-COORDCLNOOE/IDIME)
70 CONTINUE
DO 80 IEVAB-I,NEVAB
ELOADU ELEM,IEVA8) »0.0
80 CONTINUE
KGASP-O
C
"*» ENTER LOOPS FOR NUMERICAL INTEGRATION
C
DO 100 IGAUS-1,NGAUS
EXISP-POSGP(IGAUS)
DO 100 JGAUS-I,NGAUS
ETASP-POSGP(JGAUS)
KGASP-KGASP+1
C
C*** EVALUATE THE SHAPE FUNCTIONS AT THE
C
SAMPLING POINTS AND ELEMENTAL AREA
C
CALL SFRZCEXISP,ETASP)
CALL JAC0B2CIELEM,DJAC8.KGASP)
DAREA-OJACB-WEIGPCIGAUS)*WEIGP(JGAUS)
C
C««« CALCULATE LODES AND ASSOCIATE WITH
C
ELEMENT NODAL POINTS
C
DO 90 INODE-1,NNODE
NPOSN-C INODE-I)-NDOFN-I
ELOAO CIELEM,NPOSN)-ELOADCIELEM,NPOSN)♦
•SHAPE CINODE)-UDLOO-OAREA
90 CONTINUE
100 CONTINUE
110 CONTINUE
GO TO 15
115 WRI TE(I08,930)
930 FORMAT C1H0,5X,
•36H TOTAL NODAL FORCES FOR EACH ELEMENT)
DO 120 IELEM-1,NELEM
WRITEO 08.935) IELEM,
-CELOADCIELEM,IEVAB),IEVA9-1,NEVA8)
120 CONTINUE
935 FORMAT CIX,I4,5X,8E12.4/(10X,8E12.4)/
•C10X,8E12.4>)
RETURN
END
SUBROUTINE FRONT
DIMENSION FIXEDC240),EOUAT(60).VECRV(240),
• GLOADC60),GSTIF (1830),ESTIFC24,24),ELDISC3,8),
* IFFIXC240),NACVAC60),LOCEL(24),NOEST(24)
COMMON/LG0ATA/CO0RD(8O,2),PROPS(1O,4),PRESC(4O,3),
•
ASDISC240),EL0AD(24,24),N0FIX(40),
*
IFPRE(40,3).LN00SC25,8),MATN0(25)
COMMONZWORKZELCOOC2,8).SHAPE(8),DERIV(2,8),DMATX<5,5>,
«
CARTDC2,8),DBMAT<5,24),BMATX(5,24),
69
*
SM*TX(5,24/9),P0SGP(3),WEIGR(3)»
*
GPCOOC Z,9),NEROR (24)
C0MM0N/C0NTR0/NP0IN,NELEM,NN00E,N00FN,N0IME,
*
NSTRE,NTYPE,NGAUS,NPROP,NM*TS,
*
NVEIX,NEV*8,ICASE,NCRSE,:TEMP^
*
1PR0B,NPROB
COMMON/WINKLRZ
»
IEND,BMOOLS,TAREA,N0TYP,ENfLNC,
*
WINKM0C25),NDTTPEC80),EESTIf(24,24),CPSTIE(24,24),
*
3EEMAT(8),ELDISP(24,8),N0FRC (24)
COMMON/RIGID/ NRG0,MAXRGD,R£f(5),RGDND(5,8O),LNADS(25,8)
NFUNC (I,J>«(J»J-J )/2+1
MFR0N«60
MSTIE«1830
C
C*** INTERPRET FIXITY DATA IN VECTOR FORM
C
10 NT0TV«NP0IN«N00fN
DO 100 IT0TV»1,NTOTV
IFF IX(ITOTV)-O
100 FIXEDd T0TV)»0.0
IF(NVFIX.EQ.O) GO TO I15
DO 110 IVFIX-I,NVF IX
NLOCA-INOFlX(IVFIX)-D-NOOFN
DO 110 IDOFN-DNDOFN
NGASH-NLOCA-IDOFN
IFfIX(NGASH)-IFPRE (IVF IX,IDOFN)
110 FIXED(NGASH)-PRESC(IVfIX,IDOFN)
11S CONTINUE
C
C-.-CHANGE THE SIGN OF THE LAST APPERANCE
C OF EACH NODE
C
IF(NRGO.EQ.O) GO TO 118
DO 112 IELEM-I,NELEM
DO 112 INOOE-I ,NNODE
112 LNADSCIEL EM,INODE)-LNODSCIELEM,INODE)
DO 117 INODE-DNNODE
DO 117 IELEM-I,NELEM
DO 117 IRGD-DNRGD
INRGD-REF(IRGD)
DO 117 IMAX-DMA XRGD
IRIGID-RGDNDCIRGD, IMAX)
NODE-LNADS(IELEM,INODE)
IF(NODE.EQ.IRIGID) LNOOSCIELEM,INODE)»INRGO
117 CONTINUE
WRITEd 08,735)
735 FORMAT(IX/1X,' REVISED NODAL CONNECTIONS FOR RIGID BODY')
DO I19 IELEM-I,NELEM
119 WRITEO 08,725) IELEM,(LNODS(IELEM,INODE),INO0E»D NNODE)
118 CONTINUE
725 F0RMAT(1X,1X,I5,5X,8I5)
DO 140 IPOIN-DNPOIN
KLAST-O
DO I30 IELEM-DNEL EM
DO 120 INODE-1 ,NNODE
IF(IABS(LNODS(IELEM,INODE)).NE.IPOIN) GO TO 120
KLAST-IELEM
NLAST-I NODE
120 CONTINUE
130 CONTINUE
IF(KLASTaNEaO) LNODS(KLAST,NLAST)--IPOIN
70
HO CONTINUE
C
c... START BY INITIALIZING IMPORTANT QUANTITIES
C
TO ZERO
C
OO 150 ISTIF-1,MSTIF
150 GSTIF(ISTIF)=OeO
OO 160 IFRON=I,MFRON
GLOAOd FRONI=OeO
EQUAT(IFRON)=OeO
VECRVCI FRON)«0.O
160 NACVAd FRONI=O
DO 161 IPOIN=I,NPOIN
161 ASDIS(IPOIN)=OeO
C
C=== AND PREPARE FOR DISC READING AND WRITING
C
OPERATIONS
C
REWIND I
REWIND Z
REWIND 3
REWIND 4
IF(IFNDeEQeO) GO TO 162
REWIND 5
REWIND 6
162 CONTINUE
C
C=== ENTER MAIN ELEMENT ASSEMBLY-REDUCTION LOOP
C
NFRON=O
KELVA=O
DO 380 IELEM=I,NELEM
KEVAB=O
IF(IFNDeGTeO) READ (6) ESTIF I GO TO 165
READ(I) ESTIF
165 CONTINUE
DO 170 INODE=I,NNOOE
DO 170 IDOFN=I,NOO FN
NPOSI=CINOOE-D=NOOFN=IDOFN
LOCNO=LNOOSdELEM, INODE)
IF(LOCNOeGTeO) LOCELCNPOSI )=(LOCNO-I) =
« NOOFN=IOOFN
IF(LOCNOeLTeO) LOCEL(NPOS I)=(LOCNO=I)*
» NDOFN-IDOFN
170 CONTINUE
C
C=== START BY LOOKING FOR EXISTING DESTINATIONS
C
DO 210 IEVAB=I,NEVAB
NIKNO=IABS (LOCEL (IEVAB))
KEXIS=O
OO 180 IFRON=I,NFRON
IF(NIKNOeNEeNACVAdFRON)) GO TO 180
KEVAB=KEVAB=I
KEXIS=I
NOEST (KEVAB)=IFRON
180 CONTINUE
IF(KEXlSeNEeO) GO TO 210
C
C=== WE NOW SEEK NEW EMPTY PLACES FOR
C
DESTINATION VECTOR
C
71
DO I90 IFR0N»1,MfRON
IKNACVAC IFRONJ.NE.O) GO TO 190
NACVA (IFRON)«NIKNO
KEVAB-K EVABtI
NDEST(KEVAB)-IFRON
GO TO 200
190 CONTINUE
C
C«*« THE NEW PLACES MAY DEMAND AN INCREASE
C
IN CURRENT FRONTWIDTH
C
230 IF(NDESTtKEVAB),GT.NFRON) NFRON-NDEST(KEVAB)
210 CONTINUE
IF(NRGD.EO.O) GO TO 217
IALPHA-0
DO 215 IRGD-I,NRGD
DO 215 INODE-I,NNODE
215 IF(IABS (LNOOS (IELEM,INODE )).Ed.REF(IRGD)) IALPHA-IALPHAtI
IF(IALPHAeEQeO) GO TO 217
CALL TRANSF (ESTIF,IELEM)
C
C
MODIFY NECESSARY ROWS AND COLUMNS IN ESTIF
C
217 CONTINUE
C
C«tt ASSEMBLE ELEMENT LOADS
C
DO 240 IEVAB=I,NEVAB
IDEST-NDEST(IEVAB)
GLOAD(IOEST)-GLOAD(IDEST)t£LOAD(IELEM,IEVAB)
C f ASSEMBLE THE ELEMENT STIFFNESSES
C
BUT NOT IN RESOLUTION
C
IF(ICASEeGTeI) GO TO 230
DO 220 JEVAB-1,IEVAB
JDEST-NDEST(JEVAB)
IF(ESTIf(IEVAB,JEVAB).EQ.0.0) GO TO 220
NGASH-NFUNC(IBEST,JDEST)
NGISH=NFUNCtJDEST,IDEST)
IF(JOESTeGEeIOEST) GSTIF(NGASH)=
• GSTIFtNGASHjtESTIFUE VAB,JEVAB)
IF(JDEST.LT.IOEST) GSTIF(NGISH)« GSTIF(NGISH)tESTIF(IEVAB,JEVAB>
220 CONTINUE
230 CONTINUE
240 CONTINUE
C
C«*« RE-EXAMINE EACH ELEMENT NODE, TO
C
ENQUIRE WHICH CAN BE ELIMINATED
C
DO 370 IEVAB-I,NEVAB
NIKNO--LOCEL(IEVAB)
IF(NIKNO.LE.O) GO TO 370
C
Cttt FIND POSITIONS OF VARIABLES READY
C FOR ELIMINATION
C
DO 350 IfRON-1,NFRON
If(NACVAUFRON).NE.NIKNO) GO TO 350
C
C t t
EXTRACT THE COEFFICIENTS OF THE
C NEW EQUATION FOR ELIMINATION
72
I F U C A S E . G T . n GO TO 2 60
DO 250 JFR0N»1,MFRON
IF(IFRON.LT.JFRON) NLOCAaNFUNC(IFRON.J FRON)
IFCIFRON.GE.JFRON) NLOCA«NFUNC(JFRON/IFRON)
EOUAT(JFRON)«GSTIF (NLOCA)
250 GSTIF(NLOCA)aO.O
260 CONTINUE
C
C* * AND EXTRACT CORRESPONDING RIGHT
C
HAND SIDES
C
EQRHSaGLOAO(IFRON)
GLOAD(IFRON)«0.0
KELVAaKELVA+1
C
Caaa WRITE EQUATIONS TO DISK OR TAPE
C
IF(ICASE.GT.I) GO TO 270
WRITE(2 > EQUAT,EQRHS,IFRON,NIKNO
GO TO 280
270 WRITE(A) EQRHS
READ(2) EQUAT,DUMMY,IDUMM,NIKNO
280 COfiTINUE
C
Caaa DEAL WITH PIVOT
C
PIVOTaEQUAT(IFRON)
EQUAT (IFRON)»0.0
C
Caaa ENQUIRE WHETHER PRESENT VARIABLE IS
C
FREE OR PRESCRIBED
C
IFdFFIX(NIKNO).EQ.O) GO TO 300
C
Caaa DEAL WITH A PRESCRIBED DEFLECTION
C
DO 290 JFRONaI,NFRON
290 GLOAD(JFRON)aGLOAD(JFRON)-F IXEDtNIKNO)a
a EOUATt JFRON)
GO TO 3AO
C
Caaa ELIMINATE A FREE VARIABLE-DEAL WITH THE
C
RIGHT HAND SIDE FIRST
C
300 DO 330 JFRON-I,NFRON
GLOADtJFR ON)•GLOAOtJFRON)-EQUAT(JFRON>a
a EQRHS/PIVOT
C
Caaa NOW DEAL WITH THE COEFFICIENTS IN CORE
C
IF(ICASE.GT.1 ) GO TO 320
IF(EQUA T(JFRON).EQ.O.0) GO TO 330
NLOCAaNFUNC(0,JFRON)
DO 310 LFRONaI,JFRON
NGASHaLFRONtNLOCA
310 GST IF(NGASH)aGST IF(NGASH)-EQUATtJF RON)a
a EQUAT(LFRON)ZPIVOT
320 CONTINUE
330 CONTINUE
3A0 EQUATd FRONIaPIVOT
73
C*** RECORD THE NEW VACANT SPACE, AND REDUCE
C
ERONTWIDTH IE POSSIBLE
C
NACVAU FRON)"0
GO TO 360
C
C*** COMPLETE THE ELEMENT LOOP IN THE FORWARD
C ELIMINATION
C
350 CONTINUE
360 IE(NACVAINERON).NE.0) GO TO 370
NFRON*NERON-I
IF(NFRON.GT.O) GO TO 360
370 CONTINUE
380 CONTINUE
C
C*** ENTER BACK SUBSTITUTION PHASE, LOOP
C BACKWOROS THROUGH VARIABLES
C
DO 410 IELVA=T,KELVA
C
C*** READ A NEW EOUATION
C
BACKSPACE 2
READ(2) EOUAT,EORHS,IERON,NIKNO
BACKSPACE 2
IE(ICASE.E0.1) GO TO 390
BACKSPACE 4
READ(4) EORHS
BACKSPACE 4
390 CONTINUE
C
C* * PREPARE TO BACKSUBSTITUTE FROM
C
THE CURRENT EQUATION
C
PIVOT=EOUAT(IERON)
IE(IEEIXfNIKNO),EQ*1) VECRV(IERON)»
• EIXEO(NIKNO)
IEdEFIX(NIKNO).EO.O) EOUAT (IFRON)=0.0
C
C*** BACK-SUBSTITUTE INTO THE CURRENT EQUATION
C
DO 400 JFRON=T,MFRON
400 EQRHS=EORHS-VECRV(JFRON)*EOUAT(JFRON)
C
c*** PUT THE FINAL VALUES WHERE THEY BELONG
C
IEdFEIX(NIKNO).EO.O) VECRVdERON) =
» EQRHS/PIVOT
IEflEEIX(NIKNO).EQ.I) EIXED(NIKNO)-EORHS
ASDIStN IKNO =VECRVdER ON)
410 CONTINUE
IE(NRGD.EQ.O) GO TO 419
DO 404 IRGD=T,NRGD
DO 404 IELEM=T,NELEM
DO 404 INODE=I,NNOOE
IFdABSCLNODSdELEM, INODE)).EO.REF(IRGO)) GO TO 402
GO TO 404
402 NODE=LNADSUELEM, INODE)
IFCLNADSUELEM,INODE).EO.REFURGD)) GO TO 404
IDUM=3*(NODE-1)*1
ASOIS(IDUM)=O.O
74
ASDISCI0UM*1 )»0.0
ASOlSCIDUM*2)»0.0
404 CONTINUE
WRITECl08.700)
730 FORMATC IX/IX,' DISPLACEMENTS Of REFERENCE NODES AND FREE
• NODES ONLY')
DO 401 IP0IN.1,NPOIN
NGASH»IPOIN*NDOFN
NGISH=NGASH-NOOFNt I
401 WRlTECI08,920) IPOIN,CASDISCIGASH).IGASH-NGISH,NGASH)
DO 416 IELEM-1,NELEM
DO 416 INODE'1,NNODE
DO 415 IRGO-I,NRGD
DO 415 IMAX-I,MAXRGO
415 IFCIABS CLNODSCIELEM. INODE) ).ED.REf (IRGD) ) GO TO 411
GO TO 416
41I NOOE=LNATSCIELEM,!NODL)
REFNOD=REF(IRGO)
X--CCOORO(NODE,I)-COOROCREFN00.1)>
Y«COORD(NOOE.2)-COORD(REFNOD,2)
IDUM-3*(NODE-1)+1
JDUM-3* (REFNOD-1 >t1
ASOISCIDUM)»ASDIS(JDUMI-XtASDISCJDUMt1)tY«ASDIS(J0UMt2)
ASDISCI DUMtD =ASDIS(JDUMtI)
ASDISCIDUMtZ)=AS DlSCJOUMt2)
IFCIFFIX(IDUM).EQ.O) GO TO 425
FIXEDCIDUM)=FIXED(JDUM)
425 IFCIFFIXCIDUMtI).ED.0) GO TO 426
F I X E O ( I D U M t D = F I X E O( J D U M) • X t F I XEDC JDUM11 )
426 IF(FlXEDCIDUMtZ).EU.0) GO TO 416
FIXEDCIDUMt2)=FIXED(JDUM)t(-Y)tfIXEDCJOUMt2)
416 CONTINUE
DO 418 IELEM=I,NELEM
DO 418 INODE-1 ,NNODE
LNOOSCIELEM,INODE)=LNADSCIELEM,INODE)
418 CONTINUE
419 CONTINUE
WRlTECI08,900)
900 FORMAT(1H0.5X,IJHDISPLACEMENTS)
IFCNDOFN.NE.2) GO TO 4JO
IFCNDIME.NE.1) GO TO 420
WRITE(108,905)
905 FORMAT!1HO»5X,4HNODE,6X,5HOISP.,7X,
• 8HROTATION)
GO TO 440
420 WRI TE(108,910)
91O FORMAT(1H0,5X,4HNODE,SX,7HX-01SP.,
• 7X,7HY-DISP.)
GO TO 440
4JO WRITE(108,915)
915 FORMAT(1hO,5X,4HNODE,6X,5HDISP.,8X,
• 7HXZ-R0T.,7X,7HYZ-ROT.)
440 CONTINUE
DO 450 IPOIN=I,NPOlN
NGASH-I POINtNDOfN
NGISH-NGASH-NDOFNtI
450 WRI TECI08,920) IPOIN,CASDISCIGASH),IGASH=
» NGISH,NGASH)
920 FORMAT!I10.JE14.6)
WRITEO OS,925)
925 FORMATC1H0,5X,9HREACTIONS)
IFCND0FN.NE.2) GO TO 470
75
If(N0IME.NE.1> GO TO 460
WRITE(I08,930)
930 FORMAT (IH O,5X,4HNODE,6X,5HFORCE,8X,6HM0MENT)
GO TO 480
460 WRITEd 08,935)
935 FORMAT(1H0,5X,4HNOCE,5X,7HX-F0RCE,7X,
* 7HY-F0RCE)
GO TO 480
470 WRlTE(I 08,940)
940 FORMAT MHO,5X,4HNOCE,6X,5MF0RCE,6X,
» 9HXZ-M0MENT,5X,9HYZ-M0MENT)
480 CONTINUE
OO 510 IP0IN»1,NPOIN
NUOCA»(IPOIN-I>,NOOFN
OO 490 IOOFN»1,NOOFN
NGUSH«NLOCA+IDOFN
IFdFFIX(NGUSH).GT.O) GO TO 500
490 CONTINUE
GO TO 510
500 NGASH=NLOCAtNOOFN
NGISH=NLOCAtI
WRITE(I08,945) IP0IN,(F1XE0(IGASH),IGASH=
* NGISH.NGASH)
51O CONTINUE
945 FORMAT! I10,3E14.6)
C
Cttt POST FRONT-RESET ALL ELEMENT CONNECTION
C
NUMBERS TO POSITIVE VALUES FOR SUBSEOUENT
C
USE IN STRESS CALCULATION
C
OO 520 IELEM=I,NELEM
00 520 INODE=I,NNODE
520 LNOOS(IELEM,INOOE)«IABS(LNOOS(IELEM,1NOOE)>
RETURN
END
SUBROUTINE TRANSF (ESTIF,IELEM)
DIMENSION ESTIF(24,24)
C0MM0N/LG0ATA/C00R0(80,2),PR0PS(10,4),PRESC(40,3),
*
ASDIS(24O),ELOAD(24,24),NOFIX(40),
*
IFPRE(40,3>,LN00S(25,8),MATN0(25)
COMMON/WORK/ELCOD(2,8),SHAPE(8),OERIV(2,8),OMATX(5,5),
»
CARTD(2,8),D8MAT(5,24),BMATX<5,24),
*
SMATX(5,24,9),POSGP(3),WEIGP(3),
*
GPCOO(2,9),NEROR(24)
COMMON/CONTRO/NPOIN,NELEM,NNODE,NDOFN,NDIME,
*
NSTRE,NTYPE,NGAUS,NPROP,NMATS,
*
NVFIX,NEVAB,ICASEtNCASE,ITEMP,
*
IPROS,NPROB
COMMON/WINKLR/
*
IFNDtBMOOLS,TAREAtNOTYPtENFLNC,
*
WINKMO(25),NOTYPE (80),EfST IF(24,24),CPSTI F(24,24),
*
BEFMAT(8),ELOISP(24,8),NOFRC(24)
COMMON/RIGID/ NRG0,MAXRG0,REF(5),RG0N0(5,80),LNA0S(25,8)
C
C *•* MODIFY NECESSARY ROWS ANO COLUMNS IN ESTIF
C
DO 240 IRGO=I,NRGD
KOUM=O
LOUM=Q
100 CONTINUE
110 DO 220 INOOE=ItNNODE
1 F(IABS (LNODS (1ELEM, INODE)).ES.REF (IRGO) ) GO TO I30
76
GO TO 220
HO NOOE=LNAOSdELEM,INODE)
REFNOD=IABStLNOOStIELEM,INOOE))
X=-ICOOROtNODE,1>-COOROtREFNOD,I))
Y=COOROtNODE,2)-C00ROtREFNOO,2)
IDUM=3«flNOOE-1>♦)
IFtKOUMeEQ.I) GO TO HO
ElI=ELOAOtIELEM,IOUM)
EL2=EL0ADtIELEM,IOUMAl)
ELi=ELOAOtIELEM,IDUMa2)
ELOAOIIEL EM,IOUMAlI=ELZ-ELI«X
ELOAOtI ELEM,IOUMA2),(ELHY) AELi
HO CONTINUE
IFtLOUM.GE.I) GO TO 150
LLDUM=Ht INOOE-Da I
150 LOUM=LDUMAl
OO 200 JNOOE=I,NNOOE
JOUM=H IJNOOE-I )Al
IFtKOUM.ES.I) IDUM=JDUMJJDUM=H 11NOOE-I)Al
EHESTI FUDUM,IOUM)
EZ=ESTI FtJOUM,IOUMAl)
.Ei=ESTI FtJDUM,IOUM*2)
EA=ESTIFtJDUMAl,IDUM)
ES=ESTI FtJOUMAl,I0UMA1)
EG=ESTI FtJDUMA),IDUMA2)
EZ=ESTIF(J0UMA2,IDUM)
ES=ESTIFtJDUMA2,IDUMAl)
E9«ESTIFtJDUMA2,IOUMA2)
IFtKDUM.ED.I) GO TO 170
C
C*** IF KOUM=O, MODIFY COLUMNS,LOAD VECTOR,AND THE DISPLACEMENT VECTOR
C
IF KDUM=I, MODIFY ONLY THE ROWS IN ESTIF
C
ESTIFfJ OUM,IDUM)=EI
ESTlFtJDUM,IOUMAl )=I-EHX) AEZ
ESTIFfJOUM,IDUMA2)=EHY ae 3
ESTIFfjDUMAl,IDUM)=EA
ESTIFfJDUMAI,IOUMA1>=t-EA=XJAES
ESTIFtJOUMAI,IDUM*2)=EAaYAEG
ESTlF fJOUMA2,IDUM)=E7
ESTIFfJ 0UMA2,IDUMAD =I-EZ=XJAES
ESTIF tJDUMA2,I0UMA2)=E7*YAE9
GO TO 200
170 CONTINUE
ESTIFtJDUM,IDUM)=E1
ESTIFtJDUM,I0UMA1)«E2
ESTIFfJ DUM,IDUMA2) =Ei
ESTIFfJDUMAI, IDUM)=I-EHX) AEA
ESTIFfJ DUMAI,IDUMAD =I-EZ=XHES
ESTIFfJ DUMAI,IDUMA2>.f-Ei=XHEG
ESTIFtJ OUMA2,IOUMJ=EHY AE7
ESTIFtJOUMAZ,IOUNA1>=E2*YAEB
ESTIFtJ0UMA2,IDUMA2)«E3*YAE9
ZOO CONTINUE
ZZO CONTINUE
KOUM=KDUMAl
IFfKOUM.EO.D GO TO 100
ZAO CONTINUE
OO Z60 IRGO=I,NRGO
LDUM=O
OO ZSO INODE=I,NNOOE
IFtIABS tLNODStlELEM,INODE)).E0.REFtlRGO)) GO TO 221
77
GO TO 250
221 IOUM-J*(I NODC-I)*1
IKLOUM.GE.I) GO TO 222
LLDUH-I OUM
222 LDUM=LDUM+1
DO 230 JNODE=I*NNODE
IF(IABS (LNODS UELE M=JNODE)).NE.REFURGD)) GO TO 230
JDUM=3*(JNOOE-I)Al
IF(IOUM.EO.LLDUM.AND.JOUM.EQ.LLOUM) GO TO 230
IF(INODE.EO.JNOOE) GO TO 225
ESTIF(LLDUM=LLDUM)=ESTIF(LLOUM=LLDUM)
* +ESTIF(IDUM=JDUM)AEST IF(JDUM=IDUM)
ESTIF(LLDUM=LLDUMAl).ESTIF(LLDUM=LLDUMAl)
A AESTIFUDUM,JDUMA1)AESTIF(JDUM,IDUMAl)
ESTIF(LLDUM=LLDUMAZ)=ESTIF(LLDUM=LLDUM+2)
« AESTIF (IDUM=JDUMA?)AESTIF(JDUM=IDUMAZ)
ESTIF(LLDUMAl=LLOUM>«E STIF(LLDUM+1=LLDUM)
A AESTIF(IDUM*1,JDUM)AESTIF(JDUM+1=IDUM)
ESTIFULD UMAl=LLDUMAU=ESTI F(LLDUM+1,LLDUM+1 )
A AESTIF (IDUMAI=JOUMAl)AESTIF(JDUMAI,IDUMAI)
ESTIF(LLOUMAl,LLDUMAZ)=ESTIF(LLDUMAl,LLOUM+2)
A AESTIF(IDUM+I,JDUM+2)+ESTIF(JDUMAl=IDUMA2)
ESTIF(LLDUMa2,LL0UM)=ESTIF(LL0UM+2=LLDUM)
A AESTIFU DUM+2,JOUM)AESTI F(JDUM+2,IDUM)
ESTIF(LLDUM+2,LLDUMAI)-ESTIF (LLOUM+2,LLDUMAl)
* AESTIFUDUM+2,JDUMADAESTI F(JDUMAZ=IDUMAl)
ESTIF(LLDUMAZ=LLDUMAZ)=EST IF(LLDUMAZ=LLDUM+Z)
« A E S T I F ( IDUM + Z , JDUMAZ) AEST IF ( J D U M + Z , IDUMA Z)
GO TO 228
225 CONTINUE
ESTIF(LLDUM=LLOUM)=ESTIFULDUM=LLDUM)
« AESTlF (IDUM=JOUM)
ESTIF(LLDUM=LLDUMAl)=ESTIF(LLDUM,LLDUM+1)
A AESTIFU DUM=JOUMAl)
ESTl FULO UM=LLOUMaZ)=ESTlFULOUM=LLDUM+2)
* AESTIF (IDUM=JDUMAZ)
ESTIFULD UMAl,LLOUM)=E STIF(LLDUMAl,LLDUM)
* AESTIF(IDUM+I=JDUM)
ESTIF(LLDUMAl =LLDUM+1 )=ESTIF(LLDUMAl=LLDUM a I )
* AESTIFU DUMAI=JDUMAI)
ESTIF ULOUM +I,LLOUMA2>=ESTI F(LLDUMAl,LLDUM+2)
* AESTIF(IOUMAl=JDUMAZ)
ESriF(LLOUMAZ,LLDUM)«ESTlF (LLDUMAZ=LLDUM)
« +ESTIF(IOUMAZ=JDUM)
ESTIF(LLOUMAZ,LLDUMAl)=ESTIF(LL"UMAZ,LLDUMAl)
A AESTIFU DUMAZ=JDUMAI)
ESTIF(LLOUMAZ,LLDUMAZI=ESTIF(LLDUMAZ=LLDUMAZ)
« AESTIF(IDUMAZ=JDUMAZ)
228 CONTINUE
DO 229 I=IDUM=IDUM+Z
DO 229 J=JDUM=JDUM+Z
ESTIF(I=J)=O.0
229 ESTIF(J=I)=O-O
230 CONTINUE
250 CONTINUE
260 CONTINUE
RETURN
END
SUBROUTINE STREPS
C
CA** CALCULATES THE STRESS RESULTANTS AT
C
GAUSS POINTS FOR PLATE BENDING ELEMENT
73
c
DIMENSION ELDIS(3,8),STRSG(5)
COMHON/LGOATA/COORO<80,2>,PROPS(10,t),PRESCUO,3),
*
ASDIS<2tO>,ELOAO<?4,24),NOFIX(LO),
*
IFPRE<40,3),LNODS(25,8),MATN0(25)
COMMONZWORK/ELCOD(2,8),SNAPE (8),DERIV(2,8),DMATX(5.5),
*
CARTO(2,8),OBMAT(5,24),BMATX(5,24),
*
SMATX(5,24,9),POSGP(3),WEIGP(I),
*
GPC0D(2,9),NER0R(24)
COMMON/CONTRO/NPOIN,NELEM,NNODE,NOOFN,ND1ME,
*
NSTRE,NTYPE,NGAUS,NPROP,NMATS,
*
NVFIX,NEVA8,ICASE,NCASE,!TEMP,
*
IPROS,NPROB
COMMON/WINKLRZ
*
IFND,8M0DLS,TAREA,NDTYP,ENFLNC,
*
WINKMD(25),NDTTPE(80),EFSTIF(24,24),CPSTIF(24,24),
*
BEFMAT(8),ELDISP(24,8),BNOFRC(24)
WRI TEd 08,900)
WRITE(I 08,905)
C
C ** LOOP OVER EACH ELEMENT
C
DO 40 IELEM*),NELEM
C
C«*• READ THE STRESS MATRIX, SAMPLING POINT
C COORDINATES FOR THE ELEMENT
C
REAO(S) SMATX,GPCOO
WRI TE(I08,910) IELEM
C
C« * IDENTIFY THE DISPLACEMENTS OF THE
C ELEMENT NODAL POINTS
C
DO 10 INODE*),NNODE
LNOOE-L NOOS(IELEM, INODE)
NPOSN*(LNODE-))*NOOFN
DO 10 IDOFN-I,NDOFN
NPOSN-NPOSN+1
ELDISd DOFN,INODE)-ASDIS(NPOSN)
10 CONTINUE
KGASP-O
C
C*** ENTER LOOPS OVER EACH SAMPLING POINT
n
DO 30 IGAUS-I,NGAUS
DO 30 JGAUS-1,NGAUS
KGASP-KGASPd
DO 20 ISTRE-1,NSTRE
STRSG(ISTRE)-O.O
KGASH-O
C
C»** COMPUTE THE STRESS RESULTANTS
C
DO 20 INODE-1,NNODE
DO 20 IDOFN-I,NOOFN
KGASH-KGASHtI
STRSG(ISTRE)-STRSG(ISTRE)t
-SMATX(ISTRE»KGASH,KGASP)*ELDIS(IDOFN,INODE)
20 CONTINUE
C
C--- OUTPUT THE STRESS RESULTANTS
C
79
WRI TE(108,915) KGASP,
•<GPCOO(IDIME,KGASP>,IDIME«1,NOlME>,
‘(STRSG(ISTRE),ISTRE»1,NSTRE)
30 CONTINUE
40 CONTINUE
900 FORMAT(/,10X,8HSTRESSES,/)
905 F0RMAT(1H0,4HG,P.,ZX,8HX-C00RD.,2X,
•8HY-COORO.,3X,8HX-MOMENT,4X,8HT-MOMENT,
*3X,9HXY—MOMENT,2X,IOHXZ-S,FORCE,ZX,
*1OHYZ-S,FORCE)
910 FORMAT(/,5X,1 2HELEMENT NO.*,15)
915 FORMAT (15,2F10.4,5E12.5)
RETURN
END
SUBROUTINE FPRES
C0MM0N/LGDATA/C00R0(80,2>.PR0PS(10,4),PRESC(40,3),
»
ASDIS(240),EL0AD(Z4,24),NOFIX(40),
*
IFPRE(40,3),LN0DS(25,8),MATNO(25)
COMMON/WORK/ELCOD(2,8),SHAPE(8),DERIV(2,8),DMATX(5,5),
*
CARTD(2,8),DBMAT(5,24),BMATX(5,24),
*
SMAT X(5,24,9),POSGP(S),WE IGP(3),
*
GPCOD(2,9),NEROR(24)
COMMON/CONTRO/NPOIN,NELEM,NNODE,NDOFN,NOIME,
*
NSTRE,NTYPE,NGAUS,NPROP,NMATS,
*
NVF IX,NEVA9, ICASE,NCASE,ITEMP,
*
IPROB,NPROB
COMMONZWINKLR/
«
IFNO,BMOOUS,TAREA,NDTYP,ENFLNC,
*
WINKMD(25),NDTYPE(80),EFST IF(24,24 ),CPSTIF(24,24),
*
BEFMAT(8),ELDlSP(24,8),BNDFRC(24)
DIMENSION ELDSP(24 )
WRITE(I 08,820)
WRlTE(108,830)
DO 50 IELEM*1,NELEM
BMODLSbWINKMD(IELEM)
DO 5 IEVABbI,NEVAB
5 ELDSPd EVABIbO.0
READ (5) EFSTIF
WRITE(I08,810) IELEM
DO 10 IN0DE*1,NNODE
LNODEbLNOOS(IELEM, INODE)
NPOSN«(LNODE-1)*NDOFN
DO 10 IDOFN-I,NDOFN
NP0SN«NP0SN+1
D0FRDb3*( INODE-1 HlDOFN
ELDSP(DOFRDHASDIS (NPOSN)
10 CONTINUE
DO 30 1*1,NNODE
K*3*1-2
bndfrc(D beldsp(k)»bmodls
IF(EFSTIF(K,K).EQ.O.O) BNDFRC(I)*0.0
30 CONTINUE
DO 40 I«1,NNODE
LNODEbLNODS(IELEM, I)
WRITEO 08,840) LNODE,(BNDFRC(D)
40 CONTINUE
50 CONTINUE
810 FORMAT (IX/IX,'ELEMENT NUMBER :',ZX,13>
820 FORMATOX/IX,'WINKLER FOUNDATION NODE POINT FORCES')
830 FORMAT(1X/25X,'NODE',4X,'NORMAL')
840 FORMAT(IX,25X,I3,3X,EI2.4)
RETURN
80
END
SUBROUTINE CHECK I
C
C*»* TO CRITISIZE THE DATA CONTROL CARD AND
C
PRINT ANT DIAGNOSTICS
C
COMMON/LGDATA/COORO(80,2),PROPS(10»U,PRESC(A0.3),
•
ASDI SI240),EL0AD(24,24),NOFIX(AO),
»
IFPRE(40,3),LN0DS(25,8),HATN0(2S)
COHHON/UORK/ELCOO(2,8),SHAPE(8),OERIV(2,8),OMATX(5,5),
•
CARTD(2,8),0BMAT(5,24),BMATX(5,24),
•
SMATXC 5,24,9),POSGP(3),WEIGP(3),
•
GPC0D(2,9) ,NER0R(24)
commonzcontroznpoin,nele'
i,nnode,ndofn,nd ime,
•
NSTRE,NTYPE,NGAUS,NPROP,NMATS,
«
NVFIX,NEVA8,ICASE,NCASE,!TEMP,
•
IPROB,NPROB
COMMONZWlNKLRZ
•
IFND,8M0DLS,TAREA,NDTYP,ENFLNC,
•
WINKMD(25),NDTYPE(80,EFSTIF<24,24 ),CPSTI F<24,24),
‘
BEFMAT(8),ELDISP(24,8),NDFRC(24)
DO 10 IEROR*I,24
10 NEROR(IEROR)-O
C
C**» CREATE THE DIAGNOSTIC MESSAGES
C
IF(NPOIN.LE•O) NEROR(I)-I
IF(NELEM-NNODE.LT. NPOIN) NER0R(2)-1
if(nvfix.lt.i.ano.ifnd.eo.O) neror <3)»i
IFCNVFIX.GT.NPOIN) NER0R(3)»1
IF(NCASE.LE.0) NEROR(A)-I
IF(NTYPE.LT.0.0R.NTVPE.GT.2> NER0R(5)»1
IFCNNODE.LT.3.OR.NNODE.GT.8) NEROR(G)-I
IF(NDOFN.LT.2.OR.NDOFN.GT.3) NEROR(Z)-I
IF(NMATS.LE.O.OR.NMATS.GT.NELEM) NEROR<8)»I
IF(NPR0P.LT.3.0R.NPR0P.GT.5) NEROR (9)-I
IF(NGAUS.LT.2.0R.NGAUS.GT.3) NEROR (10-1
IF(N0IME.LT.1.0R.NDIME.GT.2) NEROR(II)-I
IF(NSTRE.LT.2.0R.NSTRE.GT.5) NEROR (I2)-1
C
C*** EITHER RETURN, OR ELSE PRINT THE ERRORS
C
DIAGNOSED
C
KEROR-O
DO 20 IEROR-1,12
IF(NERORdEROR).EO.O) GO TO 20
KEROR-I
WRITEd 08,900) IEROR
900 FORMAT(ZZ25H - DIAGNOSIS BY CHECKl,
• GH ERROR ,13)
20 CONTINUE
IF(KEROR.EO.O) RETURN
C
C--- OTHERWISE ECHO ALL THE REMAINING DATA
C
WITHOUT FURTHER COMMENT
C
CALL ECHO
END
SUBROUTINE ECHO
DIMENSION NTITL(SO)
COMMONZLGDATAZCOORD(80,2),PROPS(I0,4),PRESC<40,3),
•
ASOIS(240),EL0AD<24,24),NOFIX(AO),
81
*
IFPRE(40,3),LN00S<25,8),MATN0(2S)
COMMON/WORK/ELCOO(2,8)»SHAPE<8)#DERIV(Z,8).DWATX<5,5)#
*
CARTD(2s8)*DBMAT(5*?4),BMATX(S«24>,
*
SMATXC5/24,9),POSGP(I).WEIGP(3)»
*
GPCODC 2,9),NEROR(24)
Common/contro/npoin,nelem,nnode,noofn,ndime,
*
nstre,ntype,ngaus,nprop,nmats,
*
NVFlX,NEVA8,ICASE,NCASE,ITEMP,
*
IPROBfNPROB
common/winklr/
*
IEND,BMODL S,TAREA,NDTYP/ENFLNC,
*
WINKM0C25),NDTYPE C80),EFSTIFC24,24),CPST1F(24,24),
*
BEFMAT CS),ELOISPC24,8),NOFRC(24)
WRITECIOS,900>
900 FORMAT C//25H NOW FOLLOWS A LISTING 6F,
* 25H POST-DISASTER DATA CARDS/)
10 READ(105,905> NTITL
905 FORMAT!80Al)
WRITE(I08,910) NTI TL
910 F O R M A T C20X/80A1)
GO TO 10
END
SUBROUTINE CHECK2
C
C*** TO CRITICIZE THE DATA FROM SUBROUTINE INPUT
C
DIMENSION NDFR0C25)
C0MM0N/LG0ATA/C00R0(80,2),PR0PS(10,4),PRESC(40,3),
*
ASDIS(240>,EL0AD(24,24),NOFIX(40),
»
IFPRE(40,3),LNODS(25,8),MATNO(25)
C0MM0N/W0RK/ELC0D(2,8),SHAPE(8),DERIV(2,8),DMATX(5,5>,
*
CARTD(2,8),DBMATC5,24),BMATXC5,24),
*
SMATXC5,24,9),POSGP(3),WEIGP(3),
*
GPC0DC2/9) ,NER0RC24)
COMMON/CONTRO/NP01N,NELEM,NNODE,NDOFN,NDIME,
*
NSTRE,NTYPE,NGAUS,NPROP,NMATS,
*
NVFIX/NEVAB,!CASE,NCASE,ITEMP,
»
IPROB,NPROB
COMMON/WINKLR/
«
IFND,BMODLS,TAREA,NDTYP,ENFLNC,
*
WINKMD(25),NDTYPEC80),EFSTIF(24,24 ),CPSTIF(24,24),
*
3EFMAT(8),ELDISP(24,8),NDFRC(24)
MFRON-60
C
C*** CHECK AGAINST TO IDENTICAL NONZERO
C
NODAL COORDINATES
C
DO 10 IELEM-I,NELEM
10 NDFRO(IELEM)=O
DO 40 IPOIN»2,NP0IN
KPOIN=IPOIN-I
DO 30 JPOIN=I ,KPOIN
DO 20 IOIME=IfNOIME
IF(COORO( IPOIN/IDIME).NE.C00R0UP01N,
* !DIME)>G0 TO 30
20 CONTINUE
NEROR(I3)=NEROR(13)+1
30 CONTINUE
40 CONTINUE
C
C*** CHECK THE LIST OF ELEMENT PROPERTY NUMBERS
C
82
DO 50 IELEM*1 ,NELEM
50 IF(RATNO(1ELEM).LE,O.OR.M*TNO(IELEM).GT.
• NMAlS ) NEH0R(H)»NER0R<H)*1
C
C*** CHECK FOR IMPOSSIBLE NODE NUMBERS
C
OO 70 IELEM»1,NELEM
00 60 INODE-1,NNODE
IFILNODSIIELEM,!NODEI.EO.0) NEROR115)*
• NEROR I15M1
60 IFILNODSIIELEM,!NODE).LI.0.OR.LNODSIIELEM,
• INODE).61.NPOIN) NERORII6)-NEROR 116)11
70 CONTINUE
C
C« ' CHECK FOR ANT REPETITION OF A NODE
C
NUMBER WITHIN AN ELEMENT
C
DO 140 IPOIN-I,NPO IN
KSTAR-O
DO 100 IELEM-I,NEL EM
KZERO-O
DO 90 INODE-1 ,NNODE
1 FILNODStIELEM,INODE).NE.IPOIN) GO TO 90
KZERO-KZEROtI
IFIKZERO.GT.I) NER0RI17)»NER0RI17)+1
C
C“ « SEEK FIRST,LAST, AND INTERMEDIATE
C APPEARANCES OF NODE IPOlN
C
IFtKSTAR.NE.0) GO TO 80
KSTAR-IELEM
C
C--- CALCULATE INCREASE OR DECREASE IN
C FRONTWIDTH AT EACH ELEMENT STAGE
C
NOFRO IIELEM)-NDFRO 11ELEM)-NDOFN
80 CONTINUE
C
C-*- AND CHANGE THE SIGN OF THE LAST
C
APPERANCE OF EACH NODE
C
KLAST-I ELEM
NLAST-I NODE
90 CONTINUE
100 CONTINUE
IFtKSTA R.EQ.O) GO TO 110
IFlKLAS T.LT.NELEM) NDFROtKLAST-D- NOFROIKLAST-I)-NDOFN
LNODS (KLAST,NLAST )— IPOIN
GO TO I40
C
C*** CHECK THAT COORDINATES FOR AN UNUSED
C
NODE HAVE NOT BEEN SPECIFIED
C
110 WRITE1108,900) IPOIN
900 FORMAT I/I5H CHECK WHY NODE,14,
• UH NEVER APPEARS >
NEROR 118)-NEROR 118)-1
SIGMA-0.0
DO I20 IDlME-DNDIME
170 SIGMA-SIGMA-ABStCOORDtIPOIN,!DIME))
IFISIGMA.NE.0.0) NEROR(19)-NEROR119)-I
83
c
C**» CHECK THAT AN UNUSE D NODE NUMBER IS NOT
C
A RESTRAINED NODE
C
IFIIFND.GT.O.ANO.NVfIX.EQ.O) GO TO 1*0
DO I30 1VFIX«1,NVFIX
130 IF(NOFIXdVFIX).E0.1P0IN) NERORdO)*
* NEROR<20)+1
HO CONTINUE
C
C**» CALCULATE THE LARGE-ST FRONTWIDTH
C
NFRON-O
KFRON-O
DO 150 IELEM-1,NELEM
NFRON-NFRONtNDFRO(IELEM)
150 if(nfron.gt.kfron) kfron-nfron
WRITEd 08.905) KFRON
905 FORMAT(//,1X.28HMA X FRONTWIDTH ENCOUNTERED -,I5)
IF(KFRON.GT.MFRON) NEROR(ZI)-I
C
c*** continue checking the data for the fixed values
c
IF(NVFIX.EO.O.AND.IFNO.GE.I) GO TO 175
DO I70 IVFIX-I,NVFIX
IF(NOFIX(IVFIX).LE.O.OR.NOF IX(IVFlX).
• GT.NPOIN) NER0R(22)-NER0R(22)t1
KOUNT-O
DO 1 60
160
IOOFN-1,NDOFN
IFdFPR Ed VFIX, I D O F N ).GT.O>
K O U NT -I
I F (K OUN T . E Q .O ) N E R O R ( 2 3 ) » N E R O R ( 2 3 ) t 1
KVFlX-IVFIX-I
DO I 70 J V F I X - 1 , K V F I X
170 I F (IVFI X . N E . 1 . A N D . NO F I X ( I V F I X ) . E O .
• NOFIX(JVFIX)) NEROR(2C)-NEROR(24)+1
175 CONTINUE
KEROR-O
DO 180 IEROR*13,24
IF(NERORdEROR).EO.O) GO TO 180
KEROR-I
WRITE(108.910) IEROR,NEROR(IEROR)
910 FORMAT(//30H«»« DIAGNOSIS BT CHECK2, ERROR ,
* I3.6X.18H ASSOCIATED NUMBER,15)
180 CONTINUE
IF(KEROR. NE.O) GO TO 200
C
C*** RETURN ALL NODAL CONNECTION NUMBERS TO
C
POSITIVE VALUES
C
DO 190 IELEM-1,NELEM
DO 190 INODE-1,NNODE
190 LNODSd ELEM,INODE) «IABS(LNODS(IELEM,INODE) >
RETURN
200 CALL ECHO
END
O
TOTAL NO. OF PROBLEMS *
I
PROBLEM NO. I
*«* UANG AND SALMON--20.13.2 •*»
•‘INTEGRATED WINKLER FOUNDATION**
PROPERTY
I
2
I
I
I
I
I
I
I
I
I
3
I
I
I
3
I
11
9
19
17
25
32
37
42
44
50
52
58
60
NODAL POINT COORDINATES
NODE
X
Y
1
2
3
.000
.000
.000
.000
3.000
6.000
NVFIX % I9
NGAUS = 3
7
6
15
14
23
22
30
35
40
47
48
55
56
63
64
11
9
19
I7
27
25
32
37
42
SO
52
58
60
66
68
NCASE =
NOIME =
NODE NUMBERS
12 13
8
10 11
7
20 21 16
18 19 IS
28 29 24
26 27 23
33 34 31
38 39 36
43 44 41
51 52 48
53 54 49
59 60 56
61 62 57
67 68 64
69 70 65
5
3
13
11
21
19
27
34
39
44
46
52
54
60
62
I
2
NTYPE =
NSTRE =
4
2
12
10
20
18
26
33
38
43
45
51
53
59
61
SOIL MODULUS
.17500
.17500
.17500
.17500
.17500
.17500
.17500
.17500
.17500
.17500
.17500
.17500
.17500
.17500
.17500
0
5
NNOOE = 8
NEVAB = 24
NDOFN »
3
Cantilever Footing
ELEMENT
I
2
3
4
5
6
7
8
9
10
11
12
13
14
I5
NELEM * 15
NPROP = 4
Appendix C:
NPOIN « 70
NMATS = 3
4
5
6
7
8
9
10
11
I2
13
U
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
.000
.000
6.000
6.000
6.000
12.000
12.000
12.000
12.000
12.000
22. 500
22. 500
22.500
33.000
33.000
33.000
33.000
33.000
43.500
43. 500
43.500
54.000
54.000
54.000
54.000
54.000
75.333
75.333
96.667
96.667
96.667
118.000
118.000
I39.333
I39.333
139.333
160.667
I60.667
182.000
182.000
182.000
25.000
44.000
.000
6.000
44.000
.000
3.000
6.000
25.000
44.000
.000
7.000
44.000
.000
4.000
8.000
26.000
44.000
.000
9.000
44.000
.000
5.000
10.000
27.000
44.000
.000
9.500
.000
4.500
9.000
.000
8.500
.000
4.000
8.000
.000
7.500
.000
3.500
7.000
CO
Ul
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
182.000
182.000
198.500
198. 500
I98.500
215.000
215.000
215.000
215.000
215.000
222.000
222.000
222.000
229.000
229.000
229.000
229.000
229.000
245.500
245.500
245.500
262.000
262.000
262.000
262.000
262.000
23.500
40.000
.000
7.000
40.000
.000
3.500
7.000
23.500
40.000
.000
7.000
40.000
.000
3.500
7.000
23.500
40.000
.000
7.000
40.000
.000
3.500
7.000
23.500
40.000
CO
C>
RESTRAINED NODES
NODE
I
6
9
I4
I7
22
25
30
32
35
37
CODE
001
001
001
001
001
001
001
001
001
001
001
.000000
.000000
.000000
.000000
.000000
.000000
.000000
.000000
.000000
.000000
.000000
FIXED VALUES
.000000 .000000
.000000 .000000
.000000 .000000
.OOOOOO .000000
.000000 .000000
.000000 .000000
.000000 .000000
.000000 .000000
.OOOOOO .000000
.000000 .000000
.000000 .000000
AO
Ag
A7
50
55
58
63
66
001
001
001
001
001
001
001
001
.000000
.000000
.000000
.000000
.000000
.000000
.000000
.000000
.000000
.000000
.000000
.000000
.000000
.000000
.000000
.000000
.000000
.000000
.000000
.000000
.000000
.000000
.000000
.000000
NUMBER OF RIGID BODIES = 2
NUMBER OF NODES ON RIGID BOOI ES * 16
RIGID BODY NUMBER
I
Z
REFERENCE NODE
I
so
MAXIMUM NUMSc a OF NODES ON A RIGID BOOT i g
RIGID BODY
NODES
I
? Z 3 6 7 910 11
Z
SD SI SZ 55 56 58 59 60
MATERIAL PROPERTIES
NUMBER
YOUNGS MODULUS POISSON'S RATIO THICKNESS
I
•300000E*04 .Z50000E+00 .ZAOOOOEtOZ
Z
•300000E+04 .ZSOOOOEtQO .ZAOOOOEtOZ
3
•300000E +OA .2SOOOOEtOO .ZAOOOOE +02
MAX FRONTWIDTH ENCOUNTERED = 30
**• VERTICAL COLUMN LOADS ONLY
O
O
TOTAL NODAL FORCES FOR EACH ELEMENT
I
.OOOOE+00 .OOOOE+OO .OOOOE+OO
.OOOOE+OO .OOOOE+OO .OOOOE+OO
.OOOOE+00 .OOOOE+OO .OOOOE+OO
CO
UNIFORM LOAD
•OOOOOOE+00
.136000E+01
.17OOOOE+01
.OOOOE+OO
.OOOOE+OO
.OOOOE+OO
.OOOOE+OO
.OOOOE+OO
•OOOOE+OO
•OOOOE+OO
.OOOOE+OO
.OOOOE+00
.OOOOE+OO
.OOOOE+OO
.OOOOE+OO
•OOOOE+OO
•OOOOE+OO
•OOOOE+OO
.8160E»01
.00002*00
.00006*00
.0 0 0 0 6 * 0 0
.00006*00
.00006*00
.00006*00
.00006*00
. 0 0 0 0 6 *00
.00006*00
.00006*00
.0 0 0 0 6 * 0 0
.00006*00
.0 0 0 0 6 * 0 0
.00006*00
.00006*00
.00006*00
.00006*00
.00006*00
.00006*00
.00006*00
.00006*00
.00006*00
.00006*00
.00006*00
.30006*00
.00006*00
.32646*02
.00006+00
.00006*00
.00006*00
.00006*00
.00006*00
.00006*00
.00006*00
.00006*00
.00006+00
.00006*00
.00006 +00
.00006 + 00
.00006*00
.00006*00
. 00006+00
.00006+00
.00006*00
.00006*00
. 00006 +00
.00006*00
.00006 + 0 0
.00006*00
.00006+00
.00006*00
.0 0 0 0 6 * 0 0
.0 0 0 0 6 + 0 0
.00006*00
.00006*00
.00006*00
.13886*02
.00006*00
.00006*00
.00006*00
.00006*00
.00006+00
.00006+00
.0 0 0 0 6 * 0 0
.0 0 0 0 6 + 0 0
.00006*00
.00006*00
.00006*00
.00006*00
.00006*00
.00006+00
.00006*00
.00006+00
.00006+00
.00006*00
.00006+00
.0 0 0 0 6 + 0 0
. 55536 *02
.00006*00
.00006+00
.00006+00
.0 0 0 0 6 * 0 0
.00006*00
-.81606*01
.00006*00
.00006*00
.00006+00
.00006*00
.00006*00
.00006*00
.00006*00
.00006*00
.00006+00
.00006+00
.00006*00
.00006*00
.00006*00
.00006+00
.0 0 0 0 6 * 0 0
.00006*00
.00006*00
.00006*00
.00006+00
.00006+00
.00006*00
.00006+00
.00006*00
.00006+00
.00006*00
.00006+00
.00006+00
.00006*00
.00006*00
- . I 3886*02
.00006+00
.00006*00
.00006+00
.00006+00
.00006*00
.00006+00
.00006*00
.00006+00
.32646*02
.00006*00
.00006*00
.000 06 * 0 0
.00006*00
.00006*00
.00006+00
.00006+00
.00006+00
.00006*00
.00006*00
.00006*00
.00006+00
.00006*00
. 0 0 0 0 6 +00
.00006*00
.00006+00
.00006+00
.00006+00
.00006*00
.00006*00
.00006*00
.00006*00
.00006+00
.00006+00
.00006*00
.00006*00
.00036+00
.00006*00
.00006+00
.55536*02
.00006+00
.00006*00
.00006*00
.00006*00
.00006*00
.00006+00
.00006+00
.00006+00
.00006 +00
.00006+00
.00006+00
.81606*01
.00006+00
.00006*00
.00006*00
.00006*00
.0 0 0 0 6 * 0 0
.00006+00
.0 0 0 0 6 * 0 0
.00006*00
.00006+00
.00006+00
.0 0 0 0 6 * 0 0
.00006*00
.00006*00
.00006+00
.00006+00
.00006+00
.00006+00
.00006*00
.00006*00
.00006+00
.0 0 0 0 6 + 0 0
.00006*00
.00006*00
.0 0 0 0 6 * 0 0
.00006*00
.00006*00
.00006*00
.00006*00
.00006*00
.13886*02
.00006*00
.00006*00
.00006*00
.0 0 0 0 6 * 0 0
.00006+00
.0 0 0 0 6 + 0 0
.00006*00
.00006+00
.00006+00
.00006+00
.00006*00
.32646+02
.00006+00
.00006+00
.00006*00
.00006*00
.00006*00
.00006+00
.00006+00
.00006+00
.00006*00
.00006+00
.00006+00
.00006+00
.00006*00
.00006+00
.00006+00
.00006+00
.00006+00
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91.8584
8 91 .8584
9 91.8584
ELEMENT NO.=
i 101.4755
2 101.4755
3 101.4755
4 118.0000
5 118.0000
6 118.0000
7 134.5245
8 134.5245
9 134.5245
6L6M6NT NO.=
I 144.1416
2
144.1416
3 144.1416
4
160.6665
5 160.6665
6 160.6665
7 177.1913
8 177.1914
9 177.1914
3
4
5
6
7
8
9
7.2984 -.70924E*02
1.0143 -.945768+02
4.5000 -.834168+02
7.9857 -.764568+02
1.1016 -.129658+03
4.8873 -.111788+03
8.6730 -.891368+02
7
1.1143 -.156738+03
4.9436 -.170408+03
8.7730 -.187058+03
1.0707 -.164578+03
4.7500 -.167508+03
8.4293 -.I73688+03
1.0270 -.173958+03
4.5564 -.165718+03
8.0857 -.161008+03
8
1.0016 -.156078+03
4.4436 -.I58188+03
7.8857 -.I59408+03
.9580 -.144168+03
4.2500 -.145298+03
7.5420 -.145458+03
.9143 -.132346+03
4.0564 -.132448+03
7.1984 -.131498+03
9
.8889 -.112238+03
3.9436 -.111058+03
6.9984 -.110438+03
.8453 -.820158+02
3.7500 -.825748+02
6.6547 -.837558+02
.8016 -.525428+02
3.5564 -.549338+02
6.3111 -.580168+02
179296+02
234506+02
240016+02
260036+02
370586+01
778436+01
130586+02
.920446+01
.134546+01
.474156+01
.109546+02
.596956+01
.140866+02
.223126+02
601526+01
958686+01
139026+02
7 4 4 8 8 6 + 00
135646+01
277786+01
215206+01
330396+00
193086+01
.491086+01 -.841866+00
.172986+02
.472966-01
. 297096+02
.171676+01
.648676+01
.595976+00
. 137906+00
.422716+00
.623636+01
.652686+00
.649216+00
.990286+00
.471276+00
. 9 4 3 3 7 6 + 00
.321056+00
.922886+00
-.429596+00
-.823506+00
-.122236+01
.149426+00
.50 7 8 1 6 - 0 1
-.453556-01
. 2 4 5996-01
.64 1 2 7 6 - 0 1
.113626+00
374476+00
299536+00
445566+00
187896-01
795266-01
101616+00
812506+00
870586+00
663926+00
. 513016+01
. 352 376+01
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.113906+01
.123976+01
. 132166 +01
.109956+01
. 871 756 +00
.282236+01
.108686+01
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.926446+00
. 106776 + 01
.192766+01
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.21 306 6 + 01
-.124606+00
-.871986-01
-.394606-01
-.214646-01
-.255546-01
-.249286-01
.73 0 2 2 6 - 0 1
.33 6 2 3 6 - 0 1
-.640126-02
100356+01
123246+01
132186+01
848266-02
394036-01
242846+00
384486+01
417566+01
467976+01
.456596+00
.151236+01
.349166+01
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.1 2 2 8 1 6 +01
.174196+01
. 194086 +01
.305886+01
.416366+01
.246556+01
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.267556+01
.125796+01
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-.595046-02
-.421456-01
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.291736+00
.322136+00
-.131516+01
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-.158226+01
.549916+00
-.160366+01
.649296+00
-.130426+01
.723906+00
-.273986+01 -.282406+00
-.248566+01 -.592186+00
-.151996+01 -.912856+00
O
Ul
ELEMENT no.= 10
I 185.7191
.7889 -.17275E+02
2 185.7191
3.5000 -.I348SE+02
6.2111 -.95340E+01
3 185.71 91
4 198.5000
.7889 .10281E+02
5 198.5000
3.5000 .11121E+02
6 198.5000
6.2111 .12121E+02
7 211.2808
.7889 .34992E+02
8 211.2808
3.5000 .32881E+02
9 211.2808
6.2111 .3093IE+02
ELEMENT NO.= II
I 185.7191 10.7192 -.81393E+01
2 185.7191 23.5000 -.19795E+01
3 185.71 91 36.2808 .653496+01
4 198.5000 10.7192 .108776+02
5 198.5000 23.5000 .78330E+01
6 198.5000 36.2808 .714336+01
7 211.2808 10.7192 .31022E+02
8 211.2808 23.5000 .187746+02
9 211.2808 36.2808 .88805 6+01
ELEMENT NO.= 12
i 216.5778
.7889 .27581E-03
2 216.5778
3.5000 •42265E—04
3 216.5778
6.2111 .21207£-03
4 222.0000
.7889 -.26542E—04
5 222.0000
3.5000 .21621E-04
6 222.0000
6.2111 -.34038E-04
7 227.4222
.7889 .29413E-03
227.4222
3.5000 .74871 E-04
8
9 227.4222
6.2111 •I5068E—03
ELEMENT NO.* 13
I 216.5778 10.7192 .121596+02
2 216.5778 23.5000 .21469E+02
3 216.5778 36.2808 .171096+02
4 222.0000 10.7192 .123146+02
S 222.0000 23.5000 .214626+02
6 222.0000 36.2808 .169396+02
7 227.4222 10.7192 .123476+02
40820E*01
5J148E+01
65878E+01
14192E+02
14562E+02
14973E+02
12920E+02
12428E+02
11977E+02
971HEtOO
90204E*00
84332EtQ0
.261OSEtQI
•20590E*01
.14967Et01
.10356E*01
I3746E+00
13206Et01
.23330E+01
.20676E+01
.17776E+01
.18610E+01
.I9444E+01
.20166Et01
.36103E+01
.37998EtOI
.39916EtQ1
.18479Et00
.28002E+00
.38109Et00
-.34867E+00
—.16511E+00
27698E+01
43394E+01
64977E+01
12055E+02
52338E+01
99895EtOO
25854Et02
10642E+02
3981SEtOI
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-.33191E+00
.6981IEtQO
.32762E+01
.34183Et01
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•16085E+0I
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.12716Et01
.37785EtOO
.31962EtOO
.14912EtQ1
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.11301EtOO
.31925Et01
.10460EtQ1
.12677Et00
.65558EtOO
.17316E+00
-.30677E+00
—.58973E+00
-.16135 E+00
-.27086E*00
-.27521EtQI
-.10372Et01
-.40077E*00
40882E-04
11329E-05
27937E-04
37296E-06
82697E-06
10271E-OS
75980E-04
29652E-04
26418E-04
.22370E-04
-.11461E-03
.10399E-03
-. 12174E-03
-.46223E-04
.32462E-04
.77935E-04
-.20832E-04
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-.84249E-04
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-.I2992E-03
.11S43E-03
-.92596E-04
-.12281 E-03
24781E tQ2 -.21296Et01
131SIEtOZ .35954EtOO
18978Et01 .27321E+01
25547E+02 .89396E+00
13752E+02 .77175E+00
14610E+01 .53291E+00
25819EtQ2 .38970E+01
.21222E-Ol
-.I8047EtQ0
-.11003EtQO
38657E-01
-.32012E-01 -.34792E+01
.34149E-01 -.13060Et01
.37277E+00 -.37163E*00
.38582E-01 -.33758E+01
•35626E-01 -.11828E+01
-.17766E+00 -.23971E+00
.10767E+00 -.35077E+01
(Ti
8 227.4222 23.5000 .21332E+02 .13859E+02
9 227.4222 36.2808 .16647E+02 -.I5179E+01
ELEMENT NO.= 14
i 232.71 91
.7389 .33103E+02 .13'53E+02
2 232.71 91
3.5000 .3181 7E+0’ .I'.'17E+02
3 232.7191
6.2111 •30380i+02 .I2673E+02
4 245.5000
.7889 .16?1OE+02 .2. : +02
5 245.5000
3.5000 .16456E+02 .196
02
6 245.5000
6.2111 .16552E+02 .191; 12
7 258.2808
.7889 -.37087E+01 .1462«. «02
8 258.2808
3.5000 -.19295E+01 .14093E+02
9 258.2808
6.2111 -.301 06E+00 .13521E+02
ELEMENT NO.= 15
I 232.71 91 10.7192 .30008E+02 .27275E+02
2 232.71 91 23.5000 .16971E+02 .11267E+02
3 232.7191 36.2808 .95939E+01 -.33267E+01
4 245.5000 10.7192 .13548E+02 .15544E+02
5 245.5000 23.5000 .72896E+01 .63604E+01
6 245.5000 36.2808 .66909 E+01 -.14085E+01
7 258.2808 10.7192 -.18722E+01 .79742E+01
8 258.2808 23.5000 -.13517E+01 .56150E+01
9 258.2808 36.2808 .48283E+01 .46708E+01
WINKLER FOUNDATION NODE POINT FORCES
NODE
NORMAL
ELEMENT NUMBER I
I
3
•5896E-01
7
.5522E-OI
II
.5148E-Ol
I2
.5076E-Ol
I3
.4999E-0I
8
.5361E-Ol
5
.5722E-Ol
4
.5810E-01
ELEMENT NUMBER :
2
I
•5896E-01
I1633E+01 •30943E-01 -.13362E+01
16869E+01 -.73846E+00 -.42S44E+00
32009E*00
98225E*00
22491E+01
12264E+01
11532E+01
11161E+01
77898E+00
37738E+00
15699E+01
-.34246E+01
-.35809E+01
-.37914E+01
-•I2578E+01
-•I3322E+01
-.14734E+01
73664E+00
-•59205E+00
-.S2677E+00
56610E+01
13924E+00
33304E+01
30811E-Ol
I8699E+01
16569E+01
36935E+01
I85OOE+01
20456E+01
30621E+01 -.28641E+01
-.10926E+01 --10788E+01
-.33466E+00 —.42508E+00
-.11485E+01 -.10272E+01
-•32647E+00 -.29809E+00
-.24528E+00 -.24537E+00
-.43569E+00 -.21163E+00
-.31093E+00 -.19264E+00
-.45599E+00 -.39455E+00
-.12429E+00
-.95971E-Ol
-.69251E-Cl
-.23508E+00
-.24503E+00
-.26582E+00
•14745E+00
-.11522E+00
-.39563E+00
ELEMENT NUMBER :
ELEMENT NUMBER :
ELEMENT NUMBER :
S
•5522E-01
-5148E-Ol
-5148E-Ol
•5148E-01
-5522E-01
•5896E-01
•5896E-01
II
I5
I9
20
21
I6
I3
I2
•5148E-01
.4482E-Ol
•3845E-01
.3812E-01
-3745E-01
.4371E-01
.4999E-OI
.5076E-OI
9
I4
I7
I8
19
I5
II
10
.5148E-01
.4485E-01
.3851E-01
.3849E-01
.3845E-01
.4482E-OI
.5148E-01
.5148E-01
19
23
27
28
29
24
21
20
.3845E-O1
-3249E-01
-2695E-01
.2603E-01
•2523E-01
.3139E-01
.3745E-01
-3812E-01
I7
22
.3851E-01
-3254E-01
4
5
.
ELEMENT NUMBER :
6
9
10
II
7
3
2
6
VD
CD
element
element
NUMBER :
NUMBER s
ELEMENT NUMBER :
ELEMENT NUMBER :
51
52
18
44
43
.4375E-01
•4375E-01
.3717E-01
.3065E-Ol
•3064E-OI
44
48
52
53
54
49
46
45
•3065E-01
.3717E-01
.4375E-01
.4328E-Ol
.4296E-OI
.3679E-OI
•3049E-01
.3066E-31
so
55
58
59
60
56
52
51
.4375E-Ol
.4630E-01
.4885E-01
.4885E-OI
4885E-01
4630E-OI
4375E-01
4375E-OI
52
56
60
61
62
57
54
53
.4375E-01
.4630E-01
,4885E-01
.4838E-01
4802E-OI
4553E-Ol
4296E-01
4328E-OI
58
63
67
4885E-01
5437E-01
5994E-01
5995E-Ol
II
12
13
14
66
LD
ELEMENT NUMBER :
ELEMENT NUMBER :
ELEMENT NUMBER :
.2711E-Ol
•2706E-01
.2695E-OI
.3249E-Ol
.3845E-01
.3849E-01
25
30
32
33
34
31
27
26
.2711E-01
•I888E-01
.1464E-01
.1461E-01
.1455E-Ol
.I879E-0I
.2695E-01
.2706E-01
32
35
37
38
39
36
34
33
.1464E-01
.1415E-01
.1708E-0I
.I707E-01
.1703E-01
.1409E-01
.1455E-01
.1461E-01
37
40
42
43
44
4I
39
38
.I708E-OI
.2286E-01
•3063£-01
•3064E-01
.3065E-OI
.2282E-01
.1703E-01
.17Q7E-01
42
47
50
.3063E-01
.3719£-01
•4375E-01
7
8
9
10
100
ELEMENT NUMBER :
25
26
27
23
I9
I8
ELEMENT NUMBER
15
68
64
60
59
•5993E-01
.5434E-O1
.4885E-01
.4885E-Ol
60
64
68
69
70
65
62
61
.4885E-Ol
.5434E-01
.5993E-Ol
•5978E-01
.5950E-01
.5383E-OI
.4802E-01
•4838E-01
101
MONTANA STATE UNIVERSITY LIBRARIES
stks N378.H538@Theses
RL
Interaction of superstructure foundat o
3 1762 00118045 2
M A i N LIB.
N378
H538
cop.2
DATE
Hightower, J. J.
Interaction of
superstructure,
foundation, and soil
IS S U E D T O
.UR,
i