Civil Engineering Reference
In-Depth Information
z
y
6
7
2
3
x
5
8
1
4
Figure 5.46
12. Assuming “small” strains, derive the partial differential equations of 2D elastic equi-
librium under conditions of plane stress. For the square element shown in Figure 5.47
show that the stiffness matrix contains the term,
Eν
6
(
1
k
12
=
−
ν
2
)
u
6
u
7
u
3
u
2
u
1
u
4
u
8
u
5
Figure 5.47
13. Selective reduced integration (SRI) is a way of improving the performance of 4-node
plane elements as Poisson's ratio approaches 0.5 (incompressibility). The [
D
]matrix
is split into volumetric and deviatoric components, and the element stiffness matrix
