The analytical solutions for orthotropic cantilever beams (II): Solutions for density functionally graded beams

Abstract

In this paper, the specific solutions of orthotropic plane problems with body forces are derived. Then, based on the general solution in the case of distinct eigenvalues and the specific solution for density functionally graded orthotropic media, a series of beam problem, including the problems of cantilever beam with body forces depending only onz or onx coordinate and expressed byz orx polynomial is solved by the principle of superposition and the trial-and-error method.