Lab 1
LAB 1: NASTRAN INTRODUCTION AND CQUAD APPLICATIONS
Table of Contents:
Section
I.
1.1
II.
2.1
2.2
2.3
III.
3.1
3.2
IV.
4.1
4.2
I.
Title
Introduction
NATRAN History/Capability
Running NASTRAN
Process of Running NASTRAN
Printing a Hardcopy of f06 File
Syntax of NASTRAN Input Data Deck, bdf File
Examples
Input bdf File for a 2D Plate Problem
Reading NASTRAN CQUAD Output f06 File.
Assignments
In-Lab Assignments
Take-Home Assignments
Pages
1
2
2
2
7
8
13
13
23
29
30
32
Introduction
This lab chapter will serve as your introduction into NASTRAN, one of the first Finite
Element Analysis programs. You will explore how to write the input files and interpret the output
files for NASTRAN. Using the Finite Element Method, real world problems can be simplified,
modeled, and analyzed in NASTRAN to simulate the results. These results can be compared to
existing analytical solutions to check for validity. Like all computer programs, NASTRAN is
“dumb” – your results will only be as good as the input provided. By thoroughly understanding
the input you will be able to practice good modeling techniques and correctly interpret the output
the program gives. This will serve as the foundation for which the subsequent labs will build on.
Learning Objectives:
i)
ii)
iii)
iv)
Understand the role and the format of the NASTRAN input data file, bdf file
Discuss the entries of key input data cards, particularly for plate elements, CQUAD4.
Understand the NASTRAN stresses, the displacement and the reaction forces in the
output f06 file for CQUAD4: Displacements, Stresses, Support Reactions
Understand the process to print the bdf file and the f06 file.
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1.1 NASTRAN History/Capability
NASTRAN or NAsa STRuctural ANalysis was developed initially in 1966 under the
sponsorship of NASA based on known requirements of the aerospace industry for structural
analysis. The version used here, MSC/NASTRAN, has been enhanced and maintained by the
MacNeal-Schwendler Corporation which has been involved with NASTRAN since its inception.
MSC/NASTRAN is a general-purpose FEA program capable of solving a wide variety of
engineering problems. The key feature in finite element analysis is to discretize the distributed
properties of a structure into a finite number of simple substructures or elements. The physical
properties such as stiffness, inertia, conductivity, etc, are assigned to each of the elements. Grid
points connect these elements together, where point loads and constraints can be applied.
NASTRAN is mainly written in FORTRAN and currently contains over 700,000 program
statements. Some of the solving capabilities of MSC/NASTRAN include:
Linear static analysis
Static analysis with geometric and material nonlinearities
Transient analysis with geometric and material nonlinearities
Vibration and buckling analysis
Direct and modal complex eigenvalue analysis
Direct and modal frequency analysis and random response
Direct and modal transient analysis – including response spectral analysis
Linear static and vibration analysis with cyclic symmetry
Linear and nonlinear steady-state heat transfer
Transient heat transfer
Aeroelasticity
Multilevel superelements
Design sensitivity
Optimization/resizing
II. Running NASTRAN
NASTRAN always uses an extension of a filename to differentiate between files containing
data and commands. For example,
Filename.bdf
Filename.f06
Filename.log
The NASTRAN input file.
The NASTRAN output results file in text-format.
The NASTRAN file lists information about program
execution.
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Filename.op2
The NASTRAN results file in binary format ( read
by PATRAN during translation).
NASTRAN usually assigns a filename by placing a period sign (.) between the filename and
its extension. For example, the extension, ‘bdf’, denotes the NASTRAN input file. Therefore, the
file, temp.bdf, indicates an NASTRAN input file with job name, temp. Once the input file,
temp.bdf, is constructed, it can be submitted to NASTRAN for analysis.
2.1 Process of Running NASTRAN
To start NASTRAN process, click on the NASTRAN icon on the desktop. This will open a
window and call for a *.bdf file. Once the file, say temp.bdf, has been chosen, select the ‘Open’
command; the file temp.bdf will then be submitted for analysis. Wait until NASTRAN finishes
processing your job. Once done, the screen will indicate that the NASTRAN job “temp” is
completed. At this moment, NASTRAN should have produced three new output files; temp.f06,
temp.f04, and temp.log. Among these, the most important one is temp.f06 (or the f06 file) which
lists the results of the NASTRAN analysis. One may open this file using Notepad to check the
output. The end of the file should find the statement, “*** END OF JOB***”. Now take a look
to the lines just above this statement. If there is no mention of the word ERROR then your file,
temp.bdf, has been successfully analyzed by NASTRAN and the temp.f06 file contains the required
output such as the displacements and stresses. This file can be later used in viewing the results
graphically (called post-processing) using PATRAN. If there is an error, the f06 file often points
out the source of error. Correct the error and re-submit for NASTRAN analysis.
Step 1) Create NASTRAN Input Data File using Notepad or WordPad (***.bdf)
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Step 2) Save the input data file as ***.bdf
Type file name with an extension .bdf and change the file type from “Text Documents (*.txt)” to
“All Files”
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After that you can see the save file as below picture.
Step 3) Create output/result file (*.f06, *.xdb)
i. Open Nastran by clicking on it from the desktop
This will cause a window to open and will prompt for a *.bdf file.
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ii.
Once the file has been chosen, select the ‘Open’ command; the file 2D_Beam will then be
submitted for analysis. Then click ‘Run’ command. Wait until NASTRAN finishes
processing your job.
iii.
Once done, NASTRAN should have produced some new files; 2d_beam.f04, 2d_beam.f06,
2d_beam.DBALL, 2d_beam.IFPDAT, and 2d_beam.xdb. Among these, the most important
files are 2d_beam.f06 and 2d_beam.xdb which lists the result of the NASTRAN analysis
and PATRAN analysis
iv.
One may open the 2d_beam.f06 using Notepad to check the output.
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2.2 Printing a Hardcopy of f06 file
One may print out the NASTRAN bdf file following the standard printing procedure, while
print out its output in f06 file needs special attention as each output data line is jammed with 120
characters. The following is the instruction to print f06 out in a readable format. Before printing
out through Wordpad,
Step 1: Click on File>Page Setup> Change Orientation from Portrait to
Landscape
Step 2: Then change Margins like the figure for the Wordpad user
or change Margins like the figure below for the Notepad user
Step 3: Click on Font. In the Font window. Press Ctrl and A keys to select the change to
the entire document. Enter Courier for Font and Size 8 in the blank spaces on the
head bar. Then Print.
Step 4: Click on File and Print on selected printer.
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2.3 Syntax of NASTRAN Input Data Deck: bdf file
The input and output requirements for a standard finite element analysis can be listed as
follows.
Input Requirements
Nodes (Nodal numbers and coordinates), Elements (Type, geometry, thickness,
connectivity)
Material Properties, Loads, Boundary Conditions
Output Requirements
Nodal Displacement, Element Stresses, Nodal Internal Force, Reaction Forces
The NASTRAN input file (the bdf file) divides the above requirements into five sections. The
first two sections are optional. The required three sections are separated by the delimiters CEND,
BEGIN BULK and END DATA. CEND in the above file structure designates the end of the
Executive Control Section, while BEGIN BULK designates the beginning of the Bulk Data
entries. The final line in the input file must read ENDDATA. The sequence of the input file
structure is given as follows:
NASTRAN Definitions (Optional)
File Management Statements (Optional)
Executive Control Statements
(Solution types)
CEND
Case Control Commands
( Required Input and Output Options )
BEGIN BULK
Bulk Data Entries
( Finite Element Model )
ENDDATA
Optional Sections
The first optional section, NASTRAN Definitions, is only used for unusual actions. The second
optional section, File Management Statement provides means for database initialization and
management, along with job identification and restart conditions. The NASTRAN File
Management can be used to create a custom-made output file for graphic display of results that are
of interest to the user.
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Executive Control
This section is used to select the type of analysis to be performed. It also controls other general
job functions such as maximum job time and analysis alterations to a DMAP. A DMAP (Direct
Matrix Abstraction Programming) allows a user to input user-defined matrices, manipulate the
data base and output the data in the form preferred by the user. Some executive control statements
are given below.

ALTER: Used to designate the addition or deletion or both of statements in an
existing SUBDMAP.

CEND:

COMPILE: Used to specify which NDDL, or SUBDMAP, to compile.

ECHO:

ENDALTER: Used to designate the end of an ALTER.

ID:
Used to designate a job-ID for a specific run.

SOL:
Specifies the DMAP main program to be executed in this run. For
Used to designate the end of the Executive Control Section. This
statement is required unless an ENDJOB FMS statement appears in
the Executive Control Section.
Used to control print out of the Bulk Data deck.
example, SOL 101 is for static analysis, SOL 103 for vibration
analysis, and SOL 109 for transient analysis.

TIME:
Sets the maximum execution time of a job in minutes.
Case Control
The Case Control Section serves several key features for input and output. It specifies the input
load cases and the pre-scribed boundary conditions. As for output, it specifies the data to be
reported. It can report stresses, displacements, internal nodal forces, constraint reactions, etc.
Input Control
The input control of the case control section is to allow the repeated analysis of the same
structure subjected to various loadings and boundary conditions specified by the subcase
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statements. Subcases are begun by the command SUBCASE. All items placed ahead of the first
subcase will be used for all following subcases unless overridden in the individual subcase. For
static analysis, it is possible to combine subcases. This is useful for studying different loading
combinations. Some of the Case Control commands are listed below:
SUBCASE n
Example:
SUBCASE 2
Description: Delimits and identifies a subcase.
LOAD = n
Example:
Description:
SPC = n
Example:
Description:
LOAD = 300
Selects the external static load set to be applied to the structural model
where n corresponds to at least the ID number of a load entry in the Bulk
Data section.
SPC = 400
Selects the single-point constraint set to be applied to the structural model.
Parameter n refers to the ID number of a constraint entry in the Bulk Data
section. A single-point constraint assigns a fixed value to a translational or
rotational component at a geometric grid or scalar point. NASTRAN will
use the SPC conditions to eliminate unwanted degrees of freedom. One
may use PARAM, AUTOSPC, YES to eliminate all singularities found
by the Grid Point Singularity Processor (GPSP). However, this option
must be used with caution as it may cover up true design flaws. Another
helpful parameter command is PARAM, K6ROT, YES, which will
eliminate the singularity of the CQUAD element due to lack of resistance
to the in-plane rotation.
MPC = n
Example:
Description:
MPC = 500
Selects the multipoint constraint set to be applied to the structural model.
An MPC is described by a linear equation involves more than one degree
of freedom.
Output Control
TITLE = text
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Example:
Description:
TITLE = Analysis for a Cantilever Beam
The text described in the TITLE line will appear on the first line of every
output page in f06 file. If placed inside a subcase, the title will appear for
that subcase only.
SET n= a, b, c, THRU, s, EXCEPT, h, i, j, THRU, q
Example:
SET 1 = 5, 6, 7, 8, 9, 10, THRU, 55
Description: Defines lists of point numbers, element numbers, frequencies or time
steps. These sets can be used with the Physical Set Output Requests.
DISPLACEMENT = n or ALL
Example:
DISPL = 20
Description: Requests output of displacements for all or subset of physical points.
FORCE = n or ALL
Example:
FORCE = 10
Description: Requests output of forces for all or subset structural elements.
STRESS = n or ALL
Example:
STRESS = 30
Description: Requests output of stresses for all or subset of structural elements. Default
output is the Von Mises stress. The command, STRESS (MAXS) = n or
ALL, requests output of the maximum shear stress.
Notice that n in the above requests refers to the n in the SET definition. This could be used if, for
example, only the output of the displacement of a few nodal points was desired instead of the entire
model. Other useful output requests are:
GPSTRESS:
STRAIN:
GPFORCE:
SPCFORCES:
MPCFORCES:
Stresses at grid points
Strain for plate elements
Force balance for a set of grid points
Single-point forces of constraint for a set of points
Point forces for multiple point constraints
PRESSURE:
Hydroelastic pressure for a set of points
You will be able to see in the examples that Case Control commands usually reference one or more
data entries in the Bulk Data section.
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Bulk Data Deck
The Bulk Data Section starts with the delimiter, BEGIN BULK. Bulk Data entries contain
all of the information necessary to define the model. This includes geometry, element connectivity,
material properties, constraints, loadings, etc. The user must specify the geometric location of each
grid point. This is normally done with respect to a global rectangular coordinate system. Local
coordinate systems can be used to define the grid point locations, which are directly or indirectly
related to the global system. The six possible local coordinate systems are CORD1R, CORD2R,
CORD1C, CORD2C, CORD1S and CORD2S. They are referred to as the rectangular,
cylindrical and spherical systems.
Most of the input Requirements for a finite element analysis are specified in the bulk data
deck. Each command line of input has 10 entries, which can be divided by a comma. Here are
some commonly used bulk data cards. The details of each of these input cards will be discussed
later in various lab sessions.





Nodes ( Nodal numbers and coordinates )
GRID, ID,CP,X,Y,Z,CD,PS,SEID
Element Connectivity and Properties (Type, geometry, thickness, connectivity )
1D beam element
CBAR,EID,PID,GA,GB,X1,X2,X3,,+ABC
+ABC,PA,PB,W1A,W2A,W3A,W1B,W2B,W3B
PBAR,PID,MID,A,I1,I2,J,NSM,,+ABC
+ABC,C1,C2,D1,D2,E1,E2,F1,F2,+CDF
+CDF,K1,K2,I12
2D plate element
CQUAD4,EID,PID,G1,G2,G3,G4
PSHELL,PID,MID1,T,MID2
Material Properties,
MAT1,MID,E,G,NU,RHO,A,TREF,GE,+ABC
+ABC,ST,SC,SS,MCSID
Loads
FORCE,SID,G,CID,F,N1,N2,N3,AXI
Boundary Conditions
SPC,SID,G,C,D,G,C,D
SPC1,SID,C,G1,G2,G3,G4,G5,G6
MPC,SID,G1,U1, A1,G1,U2,A2
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III. Example
The example problem is a cantilever beam made of a thin plate. The length, the depth and
the thickness of the beam are 72”, 6” and 0.6”, respectively. The beam is discretized into 4
CQUAD4 elements and 10 nodes. The far left of the beam, Nodes 1 and 2 are fully constrained
and two-point loads, 100 lbs each, are applied at Nodes 9 and 10, which are the free end of the
beam. The Young’s modulus of the beam is 30x106 psi and the Poisson’s ratio is 0.33.
z
z
y
3
1
18"
1
5
2
4
7
x
3
18"
6
0.6"
9
18"
8
18"
y
6"
10
Figure 1. Example Cantilever Beam in CQUAD4
3.1 Input bdf File for a 2D Plate Problem
The bdf file of the cantilever beam problem is given below.
NASTRAN Input: beam_2d.bdf
$ EXECUTIVE CONTROL SECTION
ID ME670 BEAM2BDF
SOL 101
TIME 10
CEND
$ CASE CONTROL SECTION
SET 1=9,10
DISPL=1
STRESS=ALL
SPC=100
LOAD=100
SPCFORCES=ALL
$ BUCK DATA SECTION
BEGIN BULK
GRID,1,,0.,0.,-3.
GRID,2,,0.,0.,+3.
GRID,3,,18.,0.,3.
GRID,4,,18.,0.,-3.
GRID,5,,36.,0.,3.
GRID,6,,36.,0.,-3.
GRID,7,,54.,0.,+3.
GRID,8,,54.,0.,-3.
GRID,9,,72.,0.,3.
GRID,10,,72.,0.,-3.
SPC1,100,123456,1,2
FORCE,100,9,,100.,0.,1.,0.
FORCE,100,10,,100.,0.,1.,0.
CQUAD4,1,100,1,2,3,4
CQUAD4,2,100,4,6,5,3
CQUAD4,3,100,6,8,7,5
CQUAD4,4,100,8,10,9,7
PSHELL,100,10,0.6,10
MAT1,10,3.+7,,0.33
ENDDATA
Figure 2. NASTRAN Input bdf File
Remarks:
1, No units are specified for any data in neither input nor output in NASTRAN. It is an
user’s responsibility to prepare and interpret the data in consistent units.
2. Each command line starts with Column 1.
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3. The non-executable line starts with a $ sign.
4. Each line has up to 80 columns which are divided into ten entries. Each entry has 8
columns.
5. The above example shows a free format input in which a comma is used to divide each
entry.
6. Continuation is set in the 10th column. The first entry of the child card repeats the term
given in the 10th entry of the parent card, with the first letter or number of the term
changed to “+”.
7. The forces, the moments and the displacements are vectors.
8. Any coordinate or vector is in three dimension.
9. Any node has 6 degrees of freedom; 3 translations u, v, w , and 3 rotations
 x , y , z . That is, any node can move in 6 different ways.
10. Any model should have enough constraints to prevent it from rigid body motion.
11. A decimal point is needed for a real number
Bulk Data Deck

Nodal Coordinates
Bulk Data Entry: GRID- Grid Point
GRID,2,,1.0,-2.0,3.0
Format:
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
GRID
ID
CP
X
Y
Z
CD
PS
SEID
(10)
Example:
(1)
(2)
(3)
(4)
(5)
(6)
GRID
2
3
1.0
-2.0
3.0
(7)
(8)
(9)
(10)
316
or
GRID,2,,1.0,-2.0,3.0
This data card is written in the commonly used format, called the free format, in which a comma
is used to separate each of the data entries. This example Grid card states that the location of Grid
Point number 2 is (1.0, -2.0, 3.0 ), which is measured in terms of the global coordinate system.
The entry in column 8 indicates that the x- and z-translations and rotation about z-axis of Node 2
are constrained.
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Field
ID
CP
PS
Contents
Grid point identification number (1,000,000 > Integer > 0)
Identification number of coordinate system in which the location of the grid point is
defined (Integer  0 or blank; blank indicates that the global coordinate system is used
here.)
Location of the grid point in the coordinate system CP (Real)
Identification number of the coordinate system by which the displacement vectors and
constraint reactions are measured. (Integer  0 or blank, blank indicates that the global
coordinate system is used here.)
Permanent single-point constraints associated with the grid point of concern (any of the
SEID
digits 1-6 with no imbedded blanks) (Integer>0 or blank)
Superelement identification number (Integer>0 or blank)
X,Y,Z
CD

Element Connectivity
Bulk Data Entry: CQUAD4 – Quadrilateral Element Connection
CQUAD4,111,203,31,74,75,32,2.6,0.3,+ABC
+ABC,,,1.77,2.04,2.09,1.80
Description: Defines a quadrilateral plate element (QUAD4) of the structural model. This is an
isoparametric membrane-bending element.
Format:
(1)
(2)
(3)
(4)
(5)
(6)
(7)
CQUAD4
EID
PID
G1
G2
G3
G4
T1
T2
T3
T4
(8)
(9)
(10)
THETA/MCID ZOFFS
Example:
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
CQUAD4
111
203
31
74
75
32
2.6
0.3
1.77
2.04
2.09
1.80
or
CQUAD4,111,203,31,74,75,32,2.6,0.3,+ABC
+ABC,,,1.77,2.04,2.09,1.80
Field
Contents
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Lab 1
EID
PID
Unique element identification number (Integer > 0).
Identification number of a PSHELL entry (Integer > 0 or
blank)
Grid point identification numbers of the connection points.
(integers >0, all unique)
Material property orientation angle in degs. (Real; Default
= 0)
Material coordinate system identification number. The Xaxis of the material coordinate system is determined by
projecting the X-axis of the MCID coordinate system
G1, G2, G3, G4
THETA
MCID
(defined by the CORDij entry or zero for the basic
coordinate system) onto the surface of the element. See Fig. 2.5.
(Integer 0; if blank then THETA = 0.0 is assumed).
Offset from the surface of the grid points to the element
reference plane.
Membrane thickness of element at grid points G1 through
G4. (Real 0.0 or blank, not all zero.)
ZOFFS
T1, T2, T3, T4
 Element Properties
Bulk Data Entry: PSHELL – Shell Element Property
PSHELL,203,204,1.90,205,1.2,206,0.8,6.32,+ABC
+ABC, +0.95,-0.95
Description: Defines the membrane, bending, transverse shear, and coupling properties of thin
shell elements.
Format:
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
PSHELL
PID
MID1
T
MID2
12I/T3
MID3
TS/T
NSM
Z1
Z2
MID4
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
PSHELL
203
204
1.90
205
1.2
206
0.8
6.32
+.95
-.95
(10)
Examples:
or
PSHELL,203,204,1.90,205,1.2,206,0.8,6.32,+ABC
+ABC, +0.95,-0.95
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Lab 1
Field
PID
MID1
Contents
Property identification number (Integer >0)
Material identification number for the 17 embrane (Integer 0 or
blank)
Default value for the membrane thickness. (Real) (For a membrane
that is uniform in its thickness)
Material identification number for bending. (Integer or blank)
Bending stiffness parameter. (Real >0.0; Default = 1.0)
Material identification number for transverse shear. (Integer
T
MID2
12I/T3
MID3
0 or blank unless MID2 > 0)
Transverse shear thickness divided by the membrane thickness.
(Real > 0.0; Default = .833333)
Non-structural mass per unit area. (Real).
Fiber distances for the stress calculations. The positive direction is
determined by the right hand rule and the order in which the grid
points are listed on the connection entry.
See Remark 9 for defaults. (Real or blank)
Material identification number for membrane-bending coupling.
TS/T
NSM
Z1, Z2
MID4
See Remark 6 and 13. (Integer > 0 or blank, must be blank unless
MID1>0 and MID2 >0, may not equal MID1 or MID2).
 Materials
Bulk Data Entry: MAT1 – Material Property Definition, Form 1
MAT1,17,3.e+7,,.33,4.28,6.5e-6,5.37e+2,2.23,+ABC
+ABC,20e+4,15e+4,12e+4,1003
Description: Defines the material properties for linear, temperature-independent, isotropic
materials
Format:
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
MAT1
MID
E
G
NU
RHO
A
TREF
GE
ST
SC
SS
MCSID
(10)
Example:
(1)
(2)
(3)
(4)
(5)
(6)
17
(7)
(8)
(9)
(10)
Lab 1
MAT1
17
3.e+7
20e+4
15e+4
0.33
4.28
12e+4
or
MAT1,17,3.e+7,,.33,4.28,,,,+ABC
+ABC,20e+4,15e+4,12e+4
The Young’s modulus of the material is 3.e+7 units, Poisson’s ratio 0.33 and mass density 4.28.
The allowable tensile stress, the allowable compressive stress and the allowable shear stress are
20e+4, 15e+4 and 12e+4 units.
Field
MID
E
G
NU
RHO
A
TREF
GE
ST,SC,SS
MCSID
Contents
Material identification number (integer >0)
Young’s Modulus (Real or Blank)
Shear Modulus (Real or Blank)
Poisson’s Ratio (-1.0 < Real 0.5 or blank)
Mass density (Real)
Thermal Expansion Coefficient.(Real)
Reference temperature for the calculation of a) thermal loads, or b) a
temperature-dependant thermal expansion coefficient.
Structural element damping coefficient.
Stress Limits for tension, compression, and shear (Real). Used only to compute the
margins of safety in certain elements; they have no effect on the computational
procedures. NOTE: Margin of Safety = Factor of Safety – 1.
Material coordinate system identification number (used only in CURV
module processing; Integer 0 or blank)
 Force
Bulk Data Entry: FORCE – Static Load
FORCE,2,5,,2.9,0.0,1.0,0.0
Description: Defines a static load at a grid point
Format:
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
FORCE
SID
G
CID
F
N1
N2
N3
AXI
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
Example:
(1)
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Lab 1
FORCE
2
5
2.9
0.0
1.0
0.0
or
FORCE,2,5,,2.9,0.0,1.0,0.0
It states that a force with a magnitude of 2.9 units being applied in the positive y-direction at grid
point 5. Note that the CID entry is blank which indicates that the force vector is measured in terms
of the global coordinate system.
Field
SID
G
Contents
Load set identification number (Integer > 0)
Grid point identification number (Integer > 0)
CID
Coordinate system identification number (Integer  0, or blank; Default
= 0)
Scale factor (Real)
Components of the force vector measured in the coordinate system defined
by CID (Real; must have at least one non-zero component)
Indicates an axisymmetric loading (BCD: “AXI” or blank)
F
N1,N2,N3
AXI

Boundary Conditions
Bulk Data Entry: SPC1 – Single-Point Constraint, Alternate Form for Homogeneous Boundary
Condition
SPC1,313,123456,6,THRU,32
Description: Defines sets of homogenous single-point constraints
Format:
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
SPC1
SID
C
G1
G2
G3
G4
G5
G6
G7
G8
G9
etc..
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
SPC1
3
2
1
3
10
9
6
5
2
8
(10)
Example:
Alternative Example:
19
(10)
Lab 1
(1)
(2)
(3)
(4)
(5)
(6)
SPC1
SID
C
GID1
THRU
GID2
(1)
(2)
(3)
(4)
(5)
(6)
SPC1
313
12456
6
THRU
32
(7)
(8)
(9)
(10)
(7)
(8)
(9)
(10)
or
SPC1,313,123456,6,THRU,32
The SPC1 card number 313 states that the six degrees of freedom of nodes from 6 to 32 are
completely fixed.
Field
SID
C
Gi,GIDi
Contents
Identification number of single-point constraint set (Integer > 0)
Component number of global coordinate (any unique combination of the digits 1-6 with
no embedded blanks, when point identification numbers are grid points; must be null
if point identification numbers are scalar points)
Grid or scalar point identification numbers (Integer > 0)
Note that SPC1 is able to define constraints for more grids per entry than SPC is. Thus, it is more
generally used. SPC is needed only when the enforced displacement is not zero. Linear
combination of various boundary conditions can be imposed by the SPCD entry. Details of SPCD
can be found in the NASTRAN User Manual.
Explanation for the Input bdf of the Example Problem
Executive Control Section:
$ EXECUTIVE CONTROL SECTION
ID ME670 BEAM2BDF
SOL 101
TIME 10 (It is a static analysis which
CEND
will run NASTRAN up to 10 minutes.)
Case Control Section:
$ CASE CONTROL SECTION
SET 1=9,10
DISPL=1
STRESS=ALL
SPC=100
LOAD=100
20
Lab 1
Here we define SET 1 as Nodes 9 and 10. The next line indicates that the displacement will be
output based upon the requirement set up by SET 1. This will cause the displacements to be
output only at Nodes 9 and 10. The third line requires that the stresses be printed out for every
CQUAD element. The boundary conditions and the loading are specified based upon those stated
with SPC1 ID 100 and FORCE ID 100. To print the reaction forces at the constraint points, one
needs to insert “SPCFORCE=ALL” in the case control deck.
Bulk Data Section:
SPC1
SPC1,100,123456,1,2
Nodes 1 and 2 on the far left edge of the beam are completed fixed. It should be noticed that the
finite element model can only impose the constraint conditions at the discrete points, even
though in reality, the entire far left edge of the beam is completely fixed. The finite element
analysis does introduce errors in this regard.
GRID and CQUAD4
GRID,1,,0.,0.,-3.
GRID,2,,0.,0.,+3.
GRID,3,,18.,0.,3.
GRID,4,,18.,0.,-3.
GRID,5,,36.,0.,3.
GRID,6,,36.,0.,-3.
GRID,7,,54.,0.,3.
GRID,8,,54.,0.,-3.
GRID,9,,72.,0.,3.
GRID,10,,72.,0.,-3.
CQUAD4,1,100,1,2,3,4
CQUAD4,2,100,4,6,5,3
CQUAD4,3,100,6,8,7,5
CQUAD4,4,100,8,10,9,7
The domain is discretized into 4 elements with 10 nodes. The coordinates of each node is
specified based upon the X-Y-Z global coordinate system. The CQUAD4 entry refers to the
element thickness and material property entries PSHELL and MAT1. The last four fields of
CQUAD4 set the grid ID numbers for G1, G2, G3 and G4. For purposes of interpreting the
output, the element local coordinate system is shown in Figure 2.
21
Lab 1
Figure 2: Local Coordinate System for CQUAD Element
Remarks:
1. Element identification numbers must be unique with respect to all other element
identification numbers.
2. Grid points G1 through G4 must be ordered consecutively around the perimeter of
the element.
3. All the interior angles must be less than 180 degrees.
Since the CQUAD element used in this example is rectangular in shape. The
element x-axis is defined at the plate centroid and parallel to the line connecting G1 and
G2. The element Ye-axis is perpendicular to the Xe-axis and is in the plane of the plate. For
example, the local coordinate system of Element 1 is shown below for CQUAD4 Element
1.
Figure 3. The Local and Global
3
2
Coordinate Systems of Element 1
xe
Z
1
4
ye
X
This entry refers to a property entry. The only numerical data in this entry is the plate
thickness of .6. MAT1 specifies the Young’s module of the beam to be 30  106 and the
Poisson Ratio, 0.33.
22
Lab 1
FORCE
FORCE,100,9,,100.,0.,1.,0.
FORCE,100,10,,100.,0.,1.,0.
This load statements impose two point loads applied at Node 9 and 10; each of which is
with a magnitude of 100 lbs. and pointing toward positive Y-direction.
QUIZ: Submit the answers to the following questions in writing to the blackboard.
1. How many degrees of freedom per node in NASTRAN?
2. Based upon the following bdf files, answer the followinq questions. Note that
units are inches and pounds.
a. Coordinates of nodal point 8
b. The force vector at Node 9
c. The Local and the Global Coordinate Systems of Element 4 ( See Figure 3 as
an example for Element 1)
d. The thickness of Element 4
e. Describe the boundary condition at Node 10
GRID,7,,54.,0.,+3.
GRID,8,,54.,0.,-3.
GRID,9,,72.,0.,3.
GRID,10,,72.,0.,-3.
SPC1,100,123456,1,2
SPC1,100,6,10
FORCE,100,9,,100.,1.,0.,0.
FORCE,100,10,,100.,0.,1.,1.
CQUAD4,1,100,1,2,3,4
CQUAD4,2,100,4,6,5,3
CQUAD4,3,100,6,8,7,5
CQUAD4,4,100,8,10,9,7
PSHELL,100,10,0.8,10
MAT1,10,3.+7,,0.33
3.2 Reading NASTRAN CQUAD Output f06 File
The output options of NASTRAN static analysis are detected by the command lines
spelled in the Case Control Deck. Hereby, we will investigate the output of nodal
displacements, element stresses and constraint reaction forces, which are required
respectively by the case control deck cards: DISPL = 1, STRESS = ALL and SPCFORCES
= ALL. The NASTRAN output file of the 2D cantilever beam studied in Lab 1 will be used
here as an example to facilitate the discussion.
Output Data
Based upon the input cards in the case control deck givein in Fig. 2, output will
include displacement vectors at Nodes 9 and 10 and stresses for all CQUAD4 elements.
NASTRAN also provides a numerical error indicator, EPSILON, as a standard output.
Another common output that is important to structure design is the reaction forces at the
23
Lab 1
constrained points which can be obtained by adding a case control card, SPCFORCES =
ALL.
1) Numerical Error Inidicator
EPSILON  = 1.729E-12
In NASTRAN linear static analysis, SOL 101 aims to find the displacement
vector, x , by solving the finite element matrix equation, Kx  f , where K is the
stiffness matrix and f is the given force vector. The error indicator,

, is calculated by
In general, the accuracy of the solution is not acceptable, if the error is greater than 10-6,
  10 6 ,
2) Nodal Displacement Vector ( SET 1 = 9, 10 and DISPL = 1)
A displacement vector lists the values of 6 degrees of freedom, (u, v, w, , , ),
of each node. Only displacements at Node 9 and 10 are reported as required by the Case
Control Deck; SET 1 = 9,10 and DISPL = 1. The node type indicates that the result is
associated with a grid point, G, not a temperature, T. The values in the columns of T1, T2
and T3 are associated with the translational displacements corresponding to u, v, and w,
respectively, while those of R1, R2 and R3 corresponding to
x, 
y
, and  z , respectively.
Note that the units of the translational displacement vectors are the same as that of the
coordinates and the units of the rotational degrees of freedom are in radians. In this
example, the vertical deflection at the tip is 7.5 inches and the slopes with respect to the X
and Z axes are 0.00027 and 0.157 radians, respectively.
DISPLACEMENT VECTOR
POINT ID. TYPE
9
G
10
G
T1
T2
T3
R1
R2
R3
0.0 7.499607E+00 0.0 2.721649E-04 0.0 1.576648E-01
0.0 7.499607E+00 0.0 -2.721649E-04 0.0 1.576648E-01
The standard answer:
At Node 9, ⟨72, 0,3⟩ inches, the maximal displacement vector is ⟨0, 7.4996,0⟩ inches.
The point also rotates with 2.72E-4 radians with respect to the global X-axis and 0.1576
radians in Z-axis.
At Node 10, ⟨72, 0, −3⟩ inches, the maximal displacement vector is ⟨0, 7.4996,0⟩ inches.
The point also rotates with -2.72E-4 radians with respect to the global X-axis and 0.1576
radians in Z-axis.
24
Lab 1
3) Element Stresses
The stresses in every CQUAD4 elements are printed out, as required by the Case
Control Deck, STRESS=ALL.
STRESSES IN QUADRILATERAL ELEMENTS (QUAD4)
ELEMENT FIBRE
ID.
DISTANCE
1 -3.000000E-01
3.000000E-01
2 -3.000000E-01
3.000000E-01
3 -3.000000E-01
3.000000E-01
4 -3.000000E-01
3.000000E-01
STRESSES IN ELEMENT COORD SYSTEM
NORMAL-X NORMAL-Y
SHEAR- XY ANGLE
4.839433E+03 3.500000E+04 -1.364242E-09
-4.839433E+03 -3.500000E+04 1.364242E-09
-2.500000E+04 1.318299E+03 3.637979E-10
2.500000E+04 -1.318299E+03 -3.637979E-10
-1.500000E+04 -4.337629E+02 2.311632E-09
1.500000E+04 4.337629E+02 -2.311632E-09
-5.000000E+03 4.167526E+02 2.523848E-09
5.000000E+03 -4.167526E+02 -2.523848E-09
PRINCIPAL STRESSES (ZERO SHEAR)
MAJOR
MINOR
VON MISES
-90.0000 3.500000E+04 4.839433E+03 3.284874E+04
0.0000 -4.839433E+03 -3.500000E+04 3.284874E+04
90.0000 1.318299E+03 -2.500000E+04 2.568453E+04
0.0000 2.500000E+04 1.318299E+03 2.568453E+04
90.0000 -4.337629E+02 -1.500000E+04 1.478789E+04
0.0000 1.500000E+04 4.337629E+02 1.478789E+04
90.0000 4.167526E+02 5.000000E+03 5.220866E+03
0.0000 5.000000E+03 -4.167526E+02 5.220866E+03
As shown in the first row of the attached table, the state of stresses in the first CQUAD4
element is, in terms of the local coordinate system, on the surface with a distance
measured from the center plane as -0.3 inches along the local Ze – axis,
𝜎𝑥 = 4,839, 𝜎𝑦 = 35,000 and  x y  1.36E  9  0
in psi
(1)
Note that these results are the stresses at the center of the element and corresponding to
Fiber Distance, -0.3, as indicated in the second column of the stress output table. Besides
their magnitudes, there are many questions associated with these numbers; the units, the
meanings of x and y axes, Fiber Distance, etc.
Units
Units of the stresses are defined based upon user’s input units of the load and the
length. If the load is measured by pounds and the length by inches, the unit of a stress
quantity is psi.
Orientation of the Stresses
The orientation of the stresses is measured based upon the element coordinate system,
Xe and Ye, assigned to each of the element. This coordinate system depends upon the
connectivity of the CQUAD4 element, as shown in Fig. 3.
The input CQUAD4 card for the first element in our example is stated as
CQUAD4,1,100,1,2,3,4.
Therefore, G1 = 1, G2 = 2, G3 = 3 and G4 = 4, which result in an elemental coordinate
with Xe pointing to the global Z axis, Ye to the global X axis and Ze to the global Y axis.
Therefore, the state of stresses of CQUAD4 is shown in Figure 4. Note that the fiber
distance denoted in the output indicates the distance measured from the central plane of
the CQUAD4 element along the Ze axis. Thus, the reported stress in Element 1 are
located on the tensioned surface of the beam ( i.e., the outward normal of the surface is
facing the direction along –Y-axis.)
25
Lab 1
Xelement
x=
4.8 Kips
2
3
= 35 Kips
1
Yelement
4
Specifically, one has the state of stresses for Element 1 only as
G2=2
G3=3
x=
4.8 Kips
τXY= -1.36E-9
= 35 Kips
xe
Z
ye
G1=1
G4=4
X
Figure 4. State of Stresses at the center of CQUAD Element 1
If the input CQUAD4 card is changed to CQUAD4,1,100,1,4,3,2, the local
element axes will be changed accordingly. The resultant stresses reported in f06 file will
be changed as well. The results are listed in the following table.
STRESSES IN QUADRILATERAL ELEMENTS (QUAD4)
ELEMENT FIBRE
STRESSES IN ELEMENT COORD SYSTEM
PRINCIPAL STRESSES (ZERO SHEAR)
ID.
DISTANCE NORMAL-X
NORMAL-Y SHEAR- XY ANGLE MAJOR
MINOR
VON MISES
1
-3.000000E-01 -3.500000E+04 -4.839433E+03 1.364242E-09 90.0000 -4.83943E+03 -3.50000E+04 3.284874E+04
3.000000E-01 3.500000E+04 4.839433E+03 -1.364242E-09 0.0000 3.50000E+04 4.83943E+03 3.284874E+04
The first line of the output gives the state of stresses in CQUAD4 Element 1 as
σx= 35.0 Kpsi , σy = 4.8 Kpsi and  x y  1.36E  9  0
(2)
The output in Eq.(2) is quite different from that in Eq.(1). This difference is
caused by the change of the connectivity information, G1=1, G2=4, G3=3 and G4=2,
which results in the change in the local element coordinate system. In this case, the
elemental coordinate system, (Xe , Ye, Ze), is corresponding to the global axis system,
(X,Z,-Y). Therefore, the fiber distance 0.3 inches places the infinitesimal element on the
compressed surface of the beam.
26
Lab 1
Ye
2
3
σy = 4.8 Kpsi
σx= 35 Kpsi
1
Xe
4
Specifically, one has the state of stresses for Element 1 only as
G4=2
G3=3
y=
4.8 Kips
τXY= -1.36E-9
x=
35 Kips
ye
Z
G1=1
xe
G2=4
X
Figure 5. The State of Stresses for CQUAD4,1,100,1,4,3,2
4) Reactions at the Single Point Constraints
It is sometimes necessary to know the reactions at the constrained points defined
by SPC1 cards. These reactions can be used to investigate the strength of joining
mechanism. This can be achieved by inserting a case control deck card, SPCFORCES =
ALL For the example problem, Nodes 1 and 2 are fully constrained. As reported in the
following table, the reaction force along the Y-axis, Ry, and the reaction moments along
the X and Z axes, Mx and Mz , at Node 1 can be found as
R y  100
lbs,
M x  3,821 lb-in. and
M z  7,200 lb-in.
FORCES OF SINGLE-POINT CONSTRAINT
POINT ID. TYPE
1
G
2
G
T1
0.0
0.0
T2
-1.000000E+02
-1.000000E+02
T3
R1
R2
R3
0.0 3.821196E+03 0.0 -7..2000E+03
0.0 -3.821196E+03 0.0 -7.2000 E+03
27
Lab 1
5) Verification
It is always helpful to verify the NASTRAN results with hand calculation based upon
a simplified model. The example problem may be modeled by a cantilever beam. . The
tension stress at the center of CQUAD4 element 1 on the tensioned side of the beam
surface can be computed by the relation
x 
MC
I
where the bending moment, M, the fiber distance, C and the moment of inertia, I , are
given as
M = 200 lbs  72 inches = 14,400 lb-in.
The fiber distance is given by C = 0.3 in.
bh 3 6  0.6
I

 0.108 in4
12
12
Therefore, the tensile stress is computed as
3
x 
MC 14400  0.3

 40 ,000 psi
I
0.108
And the deflection and the slope at the free end is computed by the equation,
PL3
200  72

 7.68 in.
3EI 3  3  10 7  0.108
3
v
PL2
200  72
  v 

 0.16 radians
2 EI 2  3  10 7  0.108
2
The maximal error of 2.3% is observed in the tip displacement. The analytical tensor
stress calculated at the root of the beam is 40 kpsi which is compared with the stress of
CQUAD4 element 1, 35 kpsi. However, the stress reported in NASTRAN is at the center
of the CQUAD4, which is 9” way from the root of the cantilever beam. The associated
bending stress should be calculated based upon the moment, M = 200 lbs  63 inches =
12,600 lb-in.
x 
MC 12600  0.3

 35,000 psi
I
0.108
which matches well with the NASTRAN output.
28
Lab 1
IV. Assignments
Note on Copy and Build bdf File in Notepad:
1. Create a directory where to save the newly copied bdf file.
2. Make sure no blank in every line of the code. Save it with extension, .bdf and save
it with ‘All Files’.
3. Click on NASTRAN button, while in the directory.
4. Delete the other files besides, .bdf and .f06.
Problem Statement:
The length, the depth and the thickness of the beam are 72”, 6” and 0.6”,
respectively. The beam is discretized into 4 CQUAD4 elements and 10 nodes. The far left
of the beam, Nodes 1 and 2 are fully constrained and two point loads, 100 lbs each, are
applied at Nodes 9 and 10, which are the free end of the beam. The Young’s modulus of
the beam is 30x106 psi and the Poisson’s ratio is 0.33.
z
z
y
3
1
1
18"
5
2
4
18"
7
x
3
6
0.6"
9
18"
8
29
18"
10
y
6"
Lab 1
Submission Requirements
1. In-Lab Assignments 1 and 2:
1) Submit the bdf files and the f06 files with results onto blackboard to sign-off
the lab session.
2) We will discuss the solutions for the written assignments 1.) and 2.) of In-Lab
Assignment 1 and 4.) of In-Lab Assignment 2. These written assignments will
be turned in before the next lab session.
2. Take-Home Assignment:
Submit the bdf file and tables about displacements and reaction forces from f06
files with results to the blackboard along with the written answers to the problem
Questions before the due date..
4.1 In-Lab Assignments

Problem 1 ( to be completed in Lab ):
Two-point loads described in the above problem statement are changed to two along the
negative Z-direction, applied at Nodes 9 and 10 with a magnitude of 100 lbs each. In the
case control deck, replace the command LOAD = 100 by LOAD = 200 and add two
command lines: FORCE,200,9,,100.,0.,0.,-1. and FORCE,200,10,,100.,0.,0.,-1.
Furthermore, replace DISPL = 1 by DISPL = ALL so as to print the displacements of all
nodes. Show your bdf and f06 files to TA.
Pay attention to the stress output. The plate example can be modeled as a cantilever
beam. Find the maximal deflection of the given cantilever beam and compare your
analytical results with the NASTRAN solution in the maximal displacement and the
maximal stress.
1.) Report the displacement vectors at Nodes 7 and 8. Be sure to report the global
locations of these two nodes.
2.) Report the state of stresses at the center of CQUAD4 element 3 and plot them on
the below figure based upon the specified local and the global coordinate system.
5
7
ye
Z
xe
6
8
30
X
Lab 1
Note that the axes of the local coordinate system can be oriented differently from those
marked on the left in the above figure.

Problem 2 ( to be completed in Lab):
Modify the program to include the following three new requirements and submit it to
NASTRAN for finite element analysis. Show your bdf and f06 files to TA.
1.) The thickness and the material properties of the far left two elements are now
changed to 0.8 inches and to aluminum with E = 10x106 psi and  =0.23.
PSHELL, MAT1
2.) A roller is added to Point 6 to prevent the deflection along the z-direction; i.e.
w=0 at node 6.
SPCI
For the user of finite element analysis (FEA), it’s important to keep in mind
that every finite element node has six degrees of freedom; three translations,
u, v, w - T1,T2,T3 in f06; and three rotations,  x , y , z - R1,R2,R3 in f06.
In the SPC1 command line of the input bdf file, they are corresponding to
integers 1 to 6.


3.) Output the reaction forces by adding “SPCFORCES = ALL” in the case control
deck of the input bdf file and re-submit for NASTRAN run. The command line,
“SPCFORCES = ALL”, will require the NASTRAN to provide the boundary
reactions as output.
4.) What are the reaction forces at the fixed end and at the roller?
5.) Report the displacement vectors at Nodes 7 and 8. Be sure to report the global
locations of these two nodes.
6.) Report the state of stresses at the center of CQUAD4 element 3 and plot them on
the below figure based upon the specified local and the global coordinate system.
Z
X
Note that the axes of the local coordinate system can be oriented differently from those
marked on the left in the above figure.
31
Lab 1
4.2 Take-Home Assignment: ( Due before the next Lab Session )
This assignment helps to study the effects of mesh sizes and shapes on the accuracy of
the solution. (This homework will be due before the beginning of your next lab section )
Modify the beam_2d.bdf file (refer to Figure 2 in this lab manual on Page 13) to analyze
the following two examples and compare their results of the displacement at the tip and
the stresses at the center of the element that is closest to the left end, with the analytical
solutions based upon the simple beam theory. The magnitude of each of the forces is 500
lbf, vertical to the face of the plate.
Problem statement
The length, the depth and the thickness of the beam are 72”, 8” and 0.75”, respectively.
The two point loads, 500 lbs each, are applied as shown the below pictures. The Young’s
modulus of the beam is 30x106 psi and the Poisson’s ratio is 0.33.
Turn in the input bdf files of Problems a) and b) and write the answers of the following
questions on a separate sheet to be turned in as well.
1) Report the values and the locations of the displacement vectors at the two outer
corner points at the free end.
2) Report the state of stresses at the centers of CQUAD4 element which is adjacent
to the fixed end. Problem a) has one such element and Problem b) has two such
elements. Plot out the state of stresses in the following figures. Mark the nodal
numbers at the corners of each element. Note that the axes of the local coordinate
system can be oriented differently from those marked on the left in the following
figures.
Problem a
32
Lab 1
Problem b. First Element
Problem b. Second Element
3) Report the reaction forces at the nodes that are fixed. Two such nodes are found in
Problem a) and three such nodes in Problem b).
33