1.   Distinguish between geometric and material non-linearities. Give an example of each. Using your favorite FEM code solve the following problem:
a) assumiong linear elastic small deformation model.
b) accounting for the material and geometric non-linearities.
c) Comment on the choice of material model and effect of incorporating the geomtric non-linearity.
d) If the code permits, try different non-linear solution schemes Newton-Rhapson etc. Comment on convergence.

2. (Exercise 4 pg 474 in T. J. Hughes )

Consider  M du/dt + K d = 0

For the following variant of the Generalized trapezoidal algorithm
 

d_n+1  =  d_n + rv_n + r²/2 a_n
 M v_n+1 + K d_n+1  = 0
M a_n+1  + K  v_n+1 = 0
r is the time step (delta t)