Exact Solutions of Linear Buckling for a Class of FGM Columns with Varying Cross-Section

Abstract

This paper deals with the linear buckling problem for inhomogeneous Euler–Bernoulli column having both mechanical and geometrical properties variable along its length. Four classes of longitudinally functionally graded material columns with variable cross-sections are considered. The solutions of the relevant differential equations are obtained in terms of both hypergeometric functions and elementary functions. The normalized buckling loads are computed for five typical boundary conditions and they are validated by a comparison with approximate numerical results available in literature. The proposed formulation may provide a further benchmark for the accuracy assessment of numerical and approximated solutions.