Analysis of bidirectionally graded cylindrical beams using variational asymptotic method

Abstract

The objective of this work is to obtain closed-form analytical solutions to predict the nonlinear mechanical behavior of bidirectional functionally graded cylindrical beams accurately and faster than the commercially available finite element analysis tools. With the use of variational asymptotic method, the nonlinear three-dimensional elasticity problem is divided into a two-dimensional cross-sectional problem and a one-dimensional problem along the length of the beam. This method makes no ad hoc assumptions but rather takes advantage of small parameters inherent to the beam geometry for solving the problem in an asymptotic sense. The material properties are varied along the axial and the radial directions simultaneously using two distinct power-law parameters. Analytical results for the strains, stresses, curvatures, displacements, and sectional rotations are formulated. The results obtained under different loading conditions and material gradations using the present formulations are compared with the results obtained using three-dimensional analysis in finite element software ABAQUS.