Optimal design of functionally graded material columns for buckling problems

Abstract

This paper presents a method for improving the buckling capacity of slender columns by employing functionally graded materials (FGMs) instead of isotropic materials in constructing these members. The volume fractions of FGM constituents are varied along the column length by a trigonometric function thereby causing variations in material properties such as stiffness and density. The effective material properties are evaluated based on Mori-Tanaka scheme. The buckling problem has been solved using the finite element method (FEM) whereas optimal solution was obtained through a genetic algorithm. The present design problem considered identification of the optimal volume fraction distribution of the FGM that maximizes the critical buckling load-to-weight ratio for columnar members with different boundary conditions. The different design examples presented in this paper illustrate the effectiveness of using FGMs in constructing axially compressed columns. The present results can be successfully applied in designing FGM-columns for optimal buckling capacities.