Biomedical Engineering Reference
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(c) What are the non-zero components of
ε
and
σ
for the plane stress
case?
(d) What are the non-zero components of
ε
and
σ
for the plane strain
case?
(e) Consider the plane stress case. Let
⎡
⎣
⎤
⎦
∼
=
⎡
⎣
⎤
⎦
σ
xx
σ
yy
σ
xy
ε
xx
ε
yy
ε
xy
∼
=
.
What is the related
H
matrix for this case, using
∼
=
H
∼
?
(f)
For the plane strain case the matrix
H
is given by
⎡
⎣
⎤
⎦
+
⎡
⎣
⎤
⎦
110
110
000
4
−
20
G
3
H
=
K
−
240
003
.
Rewrite this matrix in terms of Young's modulus
E
and Poisson's ratio
ν
. Is the resulting matrix linearly dependent on
E
?
18.2 Consider the mesh given in the figure below. The mesh consists of two
linear triangular elements and a linear elasticity formulation applies to this
element configuration. The solution
∼
is given by
∼
T
=
[
u
1
w
1
u
2
w
2
u
3
w
3
u
4
w
4
],
where
u
and
v
denote the displacements in the
x
- and
y
-direction, respec-
tively.
(a) What is a possible
top
array of this element configuration assuming
equal material and type identifiers for both elements?
(b) What is the
pos
array for this element configuration?
4
3
(2)
y
(1)
x
1
2
(c) What is the
dest
array?
(d) Based on the
pos
array the non-zero entries of the stiffness matrix
can be identified. Visualize the non-zero entries of the stiffness
matrix.
