FEM for Bar

Question 1

Element stiffness matrix for a two-node bar element

Answer 1

k = integral 0-L (EAB^T B )dx

Question 2

Approximate solution may be represented by a n’th order polynomial

Answer 2

u = u(x) sum Ni(x) * vi = Nv

Question 3

Lagrange first order polynomial

Answer 3

Ni(x) = li^n(x) = (x-xj)/(xi-xj)

Question 4

Natural coordinates for an one dimentional element

Answer 4

-1 at the first node, 0 halfway and 1 at the last node

Question 5

What is the B matrix

Answer 5

B = strain displacement matrix

Question 6

What is the Jacobian determinant, J?

Answer 6

Scaling factor that transforms the physical length dx associated with a reference length.

Question 7

What is the Jacobian for a 1D element with length L?

Answer 7

The Jacobian is L/2

Question 8

Fe solution to stress and displacement, which is exact at nodes and which is exact between nodes

Answer 8

FE stress are exact at nodes

FE displacement is exact between nodes

Question 9

Can improve the accuracy of the FE solution by

Answer 9

Increasing number of elements

Increasing the polynomial order of the interpolant