FE Solution

Question 1

FE solution is represented by

Answer 1

Displacement (u=Nv)
Strains (epsilon = Bv)
Stressed (sigma = CBv)
Nodal forces (S = kv + S^o)

Question 2

FE solution always satisfies

Answer 2

Nodal point equilibrium

Wlement equilibrium

Question 3

Displacement satisfy compatibility at

Answer 3

Nodes
Within elements
At interelement boundaries

Question 4

Completeness criterion

Answer 4

N have to be complete to the m’th order, where m defines the order if the strain-displacement differential operator

Question 5

Compatibility criterion

Answer 5

The nodal dofs v, have to be chosen such that C^(m-1) continuity is obtained for all nodes

The polynomials in the shape function N have to be chosen such that C^(m-1) continuity is obtained across all inter-element boundaries

Question 6

Tests to assess convergence of displacement-type elements

Answer 6

1. Ridgid body motions without self-straining
2. The number of zero eigenvalues for the element stiffness matrix corresponds to the number of ridgid body modes
3. Patch test
4. Individual element test
5. Single element test

Question 7

What is the equation for the error given by Taylor expansion

Answer 7

O(h(p+1))

Question 8

Strains or stresses converge with an error of

Answer 8

O(h(p+1-m))

Question 9

Strain energy will show an error of

Answer 9

O(h(2(p+1-m)))

Question 10

The order of FE mesh error can be reduced by

Answer 10

1. Reducing the characteristic length of an element, h.

2. Increasing the degree of highest complete polynomial N