# ME 422 Exam 2 Do all 6 problems Name Problem 1

```ME 422 Exam 2
Do all 6 problems
Name
Problem
Problem
Problem
Problem
Problem
Problem
TOTAL
1
2
3
4
5
6
(5
(5
( 18
( 18
( 18
( 36
)
)
)
)
)
)
(100)
1
Problem 1 Consider the equation
M
F
| {zṪ} + KT
| {z } = |{z}
I
II
III
In a steady-state (static) finite element heat conduction analysis, which term is always unnecessary:
(a) I
(b) II
(c) III
(d) None of the above
Problem 2 In a static stress analysis without gravity loading, which properties are always
unnecessary?
(a) E (Young’s modulus)
(b) I (moment of inertia)
(c) ρ (density)
(d) ν (Poisson’s ratio)
(e) G (shear modulus)
(f) A (cross-sectional area)
(g) None of the above – they’re all important.
2
Problem 3 Consider the linear elasticity plane stress element shown below. What is M13
for this element? Set up all integrals as completely as possible but do not integrate.
y
(0,2)
(1,2)
1
2
ρ
3
(0,0)
4
(1,0)
3
x
Problem 4 A single truss (bar) element is used to model the transient motion of the structure
shown below. Set up the global system of equations for this situation, applying all boundary
conditions appropriately.
E,A
ρ
F
F
L
bar element
4
Problem 5 A single beam element is used to model the transient motion of the structure
shown below. Set up the global system of equations for this situation, applying all boundary
conditions appropriately.
E,A,I
ρ
F
F
L
beam element
5
Problem 6 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.
(a) What is the heat flux vector
&quot;
#
q̇x′′
′′
q̇ =
q̇y′′
evaluated at x = 0, y = 0 in element 1?
(b) What is the heat flux vector evaluated at x = 0, y = 0 in element 2?
y
W
0
0
2
conductivity
k
1
0
Tc
H
0
0
0
L
6
0
0
x
```