AAE 558, Fall 2011, Homework #8 Feedback
100 points distributed as follows:
Problem 125 pts
Problem 2.25 pts
Problem 325 pts
Problem 425 pts
Comments:
In Problem 4, [f] is not the nodal flux. The fluxes will have two components for
a 2D problem (x, y) and

AAE 558, Fall 2011, Homework #10
1. Construct row 1 of the
matrix for the six-node triangle.
a. Show that for the rigid body translation
strain vanishes.
b. Let the nodal displacements be proportional to the coordinates, i.e.
the strain field. Does this a

AAE 558, Fall 2011, Homework #9
1. Consider a triangular panel made of tow isotropic materials with thermal
conductivities of
and
as shown in Figure 1. A constant
is prescribed along the edge BC. The edge AB is insulated
temperature of
and a linear distri

AAE 558, Fall 2011, Homework #5 Feedback
100 Points distributed as following:
1. Problem 150 pts (10 pts for each part)
2. Problem 250 pts (25 pts for each part)
i. Number of Gaussian points 5 pts
ii. Relation between x and 5 pts
iii. Final answer obtaine

AAE 558, Fall 2011, Homework #5
1. Consider a four-node cubic element in one dimension. The element length is 3 with
; the remaining nodes are equally spaced.
a. Construct the element shape functions.
b. Find the displacement field in the element when
c.

AAE 558, Fall 2011, Homework #4
1. Given the strong form for the heat conduction problem in a circular plane:
natural boundary condition:
essential boundary condition:
where
is the total radius of the plate. is the heat source per unit length along the
pl

AAE 558, Fall 2011, Homework #6
1. Given a one-dimensional elasticity problem as shown in Figure 1. The bar is
)
constrained at both ends (A and C). Its cross-sectional area is constant (
on segment AB and varies linearly A=0.5(x-1) m2 on BC. The Youngs m

AAE 558, Fall 2011, Homework #7 Feedback
100 points distributed as follows:
Problem 150 pts
Problem 250 pts
Comments:
Again, like for the one-dimensional problems, the weight function is assumed to be zero along
the essential boundary.

AAE 558, Fall 2011, Homework #7
,
1. Given a vector field
Verify the divergence theorem.
on the domain ABCD shown in Figure 1.
Figure 1 Domain for Problem 1 (
are normals)
2. The two-dimensional constitutive relation for the heat conduction problem (Fouri

AAE 558, Fall 2010, Exam#1 Solution
Problem 1:
(a)
Multiply the governing equation and the natural boundary condition by an arbitrary
weight function (1 pt)
[
(
)
(
()
)|
Integration by parts (2 pt)
[
(
(
()
]
Consider
(
()
)
(
)|
()
]
)
(2 pt) and subst

AAE 558, Fall 2010, Exam#2 Solution
Problem 1:
Multiply the governing equation by an arbitrary weight function (5 pt)
Apply divergence theorem (5 pt)
Divide the whole boundary into , and (5 pt)
For , (5 pt), For , , For , (5 pt)
Substitute Fouriers law (

AAE 558, Fall 2010, Exam#2 Solution
Problem 1:
Multiply the governing equation by an arbitrary weight function (5 pt)
[
)
Divide the whole boundary ( ) into
(
For
(
)
(
(
(
Apply divergence theorem (5 pt)
]
,
)
and
(5 pt)
(5 pt), For
)
,
)
, For
,
(
(
,

Exam #1
AAE-558: Start 1:30 PM, Ends: 2:20 PM Friday September 24, 2010
Problem 1: Show that the weak form of
d
du
AE 2 x 0 on 1 x 3
dx
dx
du
0.1,
dx x 1
u 3 0.001
1 E
is given by
3
3
dw
du
dx AE dx dx 0.1(wA) x1 2 xw dx w with w(3) 0
1
1
(7 poi

P=100 N
y
x
P=100 N
All angles are with respect to positive x axis.
For this problem and for the give loading type
1. Use a finite element code of your choice to calculate deflection of all members of both truss
structures using 3-D truss elements. (40 po

Exam #2
AAE-558: Start 1:30 PM, Ends: 2:20 PM Friday November 12, 2010
(30 points) Problem 1: Consider a heat conduction problem in 2D with boundary
convection in the figure above. Construct the weak form for heat conduction in 2D for the
above problem. R

AAE 558, Fall 2011, Homework #1
1. For the spring system given in Figure 1.
a.
b.
c.
d.
Number the elements and nodes.
Assemble the global stiffness and force matrix.
Partition the system and solve for the nodal displacements.
Compute the reaction forces.

AAE 558, Fall 2011, Homework #1 Feedback
100 Points are distributed as following:
1. Problem 1.20 pts
a. Number elements and nodes4 pts
b. Global stiffness and force matrix8 pts
c. Nodal displacement4 pts
d. Reaction forces4 pts
2. Problem 2.40 pts
a. Num

AAE 558, Fall 2011, Homework #2 Feedback
100 Points are distributed as following:
1. Problem 140 pts
a. 10 pts
i. Nodes and elements setting2 pts
ii. Stiffness of each element2 pts
iii. Global stiffness and force matrix2 pts
iv. Displacement2 pts
v. Perce