ME 422 Exam 2
Do all 9 problems
Name
Problem
Problem
Problem
Problem
Problem
Problem
Problem
Problem
Problem
TOTAL
1
2
3
4
5
6
7
8
9
(12)
(4)
(4)
(4)
(4)
(4)
(25)
(25)
(18)
(100)
1
Problem 1
(a) The 4-node isoparametric finite element shown below has
(i) γxy > 0
(ii) ǫxx > 0
(iii) ǫyy > 0
(iv) All of the above
(v) None of the above
y
x
(b) The 4-node isoparametric finite element shown below has
(i) γxy > 0
(ii) ǫxx > 0
(iii) ǫyy > 0
(iv) All of the above
(v) None of the above
y
x
(c) The 4-node isoparametric finite element shown below has
(i) γxy > 0
(ii) ǫxx > 0
(iii) ǫyy > 0
(iv) All of the above
(v) None of the above
y
x
2
Problem 2 For a static (steady) finite element heat transfer analysis, we must define the
following properties to get realistic answers:
(a) k
(b) ρ
(c) cp
(d) All of the above
Problem 3 For a transient (unsteady) finite element heat transfer analysis, we must define
the following properties to get realistic answers:
(a) k
(b) ρ
(c) cp
(d) All of the above
Problem 4 Consider the equation
M
F
| {zÜ} + KU
| {z } = |{z}
I
II
III
In a static finite element analysis, which term is always unnecessary:
(a) I
(b) II
(c) III
(d) None of the above
Problem 5 Which is the correct global forcing vector for the finite element beam system
shown below? (Assume that the beam nodes have rotations and vertical displacements as
unknowns.)
M
clamped
clamped
1
(a) FT =
(b) FT =
(c) FT =
h
0 0 0 0
h
M L M −M L −2M L
h
h
i
0 M 0 0
i
(d) FT = M L 0 0 −2M L
(e) None of the above
i
2
3
i
3
4
Problem 6 The hoop stress τθθ is important in which type of finite element analysis?
(a) Plane stress
(b) Plane strain
(c) Axisymmetric
(d) Fully 3-D
(e) All of the above
(f) None of the above
Problem 7 Consider the object shown on the left below , which was initially hot but has now
been surrounded by ice on its four edges. The finite element model of the object is shown on
the right below. The center temperature is currently Tc , and the outer node temperatures
are all zero. What is the current value of the total rate of heat loss out of the object, as
predicted by the finite element method? (We have often denoted the total rate of heat loss
as Q̇.)
W
0
0
0
conductivity
k
Tc
H
0
0
0
L
4
0
0
Problem 8 Consider the linear elasticity plane stress element shown below. If Poisson’s
ratio (ν) is zero, what is K13 for this element? Set up all integrals as completely as possible
but do not integrate.
y
(0,2)
2
E
1
(1,1)
3
x
(0,0)
5
Problem 9 Consider the truss element shown below, which has a Young’s modulus of E.
Recall that the transformation matrix for a truss element is
"
δ1
δ2
#
=
"
cos α sin α
0
0
0
0
cos α sin α
#





u1
v1
u2
v2





 = T


If the deflections of the bar are given by





u1
v1
u2
v2






=


a
0
a
1
a
2





then what is the stress in the truss?
v2
L
u2
v1
45o
u1
6

u1
v1
u2
v2




