[ANSWERED] 1. Derive the stiffness matrix for the non prismatic bar shown in Figure P3–53 using the principle..

1. Derive the stiffness matrix for the non prismatic bar
shown in Figure P3–53 using the principle of minimum potential energy. Let E be
constant.
2. For the bar subjected to the linear varying axial load
shown in Figure P3–54, determine the nodal displacements and axial stress
distribution using (a) two equal-length elements and (b) four equal-length
elements. Let A = 2 in.
2
and E =30 10
6
psi. Compare the
finite element solution with an exact solution.