We will focus on the 1D bar . Develop a MATLAB program to solve:

(EAu;x ) ;x +q(L - x) = 0

u(0) = u

EAu;x (L) = P

1. Compute the FEM matrix equations for the 1D bar study,

i.e., find K and P using you element stifness and loads develop. This will require an appropriate Gauss Quadrature rule.

2. Using the values

EA = 1

q = 1

u = 0

P = 1

L = 1

Do the following for 1,2,4 and 8 element discretizations(use even node spacing):

(a) Solve the linear equations for the nodal displacements

(b) Plot the solution

3. Repeat Part 2 using the values

EA = cos(x/2L)

q =1/2

u = 1

P = 2

L = 5

4. Select several non-uniform meshes to solve the following problem:

(EAu;x ) ;x +q(x) = 0

u(0) = 0:15

u(L) = 0:1

EA = 10x

q(x) = -exp(-x/L)

L = 8