Plane Stress Problems

Question 1

Assumptions

Answer 1

1. Body (volume) forces F do not vary over thickness, and have no component in z-direction
2. surface tractions are constant over the thickness of the boundary and do not have components in the z-direction
3. only in-plane loading

Question 2

Strong form defined by

Answer 2

Equilibrium
Material las
Natural boundary conditilns
Essential boundary conditions

Question 3

What form is FEM based on?

Answer 3

The weak form

Question 4

Principle of virtual displacement (PVD)

Answer 4

Internal virtual work = external virtual work (body forces*surface tractions)

Question 5

Element stiffness matrix k expressed as

Answer 5

k = (integral over V) B^T CB dV

Question 6

S^o have contributes from

Answer 6

Sf^o = body forces

S_phi ^o = surface traction

Question 7

Natural coordinates for quadeilateral elements expressed by

Answer 7

Zeta and eta, from -1 to 1

Question 8

What are Serendipity elements

Answer 8

Internal nodes are avoided (except for elements of quartic order or higher)
Often more efficient compared to lagrange