A cantilever beam is made by connecting two rods together. The left half, , of the beam has properties, , and , and the right half, , has properties, , and . The beam is subjected to a distributed load, and a horizontal load at the free end, P. The length of the beam is denoted as . Assume that the material is linear elastic and the beam follows the linear strain-displacement relation. The beam is fixed at Thus, it is with given boundary conditions, u(0)=w(0)=w^' (0)=0. The displacement field of the beam is assumed as: