MAE M256B, CEE M230B
HW #1 - Solution
Problem 1
A is a second nonsingular order tensors in a 3-dimensional space. Let
B = AA T and C = A T A.
(a) Show that B2 = ACA T and C2 = A T BA .
B2 = BB = AA T
More Hints on HW #5
Problem 8.1
Assume that A < X1 < 4A (instead of 5A).
The material is Neo-Hookean and the outer surface is traction free. Calculate the traction
components on the flat end sections
MAE 256B, CEE 230B, HW #5 with hints
Reader Problem 8.1 (modified)
Assume that A < X1 < 4A (instead of 5A).
In (c) assume that the material is of the Mooney-Rivlin type and the outer surface is
tracti
MAE M256B, CEE M230B, HW #4
Problems 7.1, 3, 4, 5
Problem 7.5 (Hints)
W I W II W III
ij =
+
+
I ij II ij III ij
I
II
III
= ij , = I ij ij ,
= II ij I ij + ik kj
ij
ij
ij
ij
approx
= (2c1I + 3c3I 2
MAE M256A, CEE M230A, HW #4 Solution
Problem 7.1
B = FFT = (I + H)(I + H T ) = I + H + H T + HH T = I + 2 + s
B I = 2 + s
1
I B = trB = 3 + 2I H + Is , where = (H + H T ), s = HH T
2
a) In the linear
MAE M256B, CEE M230B
HW #3-Solution
6.3
PF + H = K + UdVt
Vt
PF = K + ijv i, jdVt (Eq. 6.51), H = hdVt q i n ids
Vt
Vt
St
hdVt q i n ids + ijv i, jdVt UdVt = 0
Vt
St
Vt
Vt
1
1
1 dV
dVt
= F ij = FiI
MAE M256B, CEE M230B
HW #3
Course Reader Problems 6. 3, 4, 5.
Hints:
6.3
Global Equation: PF H K UdVt
Vt
where PF K ij vi, jdVt and H hdVt q i n i ds
Vt
Vt
St
Local form:
FiI Ij vi,J G Jj 0 h (Jq i G
HW #2 Solution
MAL
Problem 1 (5.3)
x1 = X1e t + X3 (e t 1), x 2 = X 2 + X3 (e t e t ), x 3 = X3
t
t
t
t
X1 = x1e x 3 (1 e ), X 2 = x 2 x 3 (e e ), X3 = x 3
et
J= 0
0
0
(1a)
(1b)
et 1
1 e t e t = e t >
MAE M256B, CEE M230B
HW #2
Problem 1. Modified 5.3 in Reader
For the given motion show that J 0 and obtain the material and spatial descriptions of the
velocity and acceleration fields.
Problem 2. Pro
MAE M256B, CEE M230B
HW #1
Problem 1
A is a second nonsingular order tensors in a 3-dimensional space. Let
B = AA T and C = A T A.
(a) Show that B2 = ACA T and C2 = A T BA .
(b) Write all four equatio