Abstract
This article presents a study of multiobjective shape optimization of nonuniform microbeams made of functionally graded materials (FGMs). The goal is to discover the optimal shape functions and volume fraction distribution to maximize the critical buckling load and fundamental frequency while minimizing the mass and material cost of the microbeam. Based on Timoshenko beam theory with the modified couple stress theory, the static and dynamic behavior of axially functionally graded material nonuniform microbeam has been presented. Three types of shape functions are considered to control the variation of height and width along the beam length. The multiobjective particle swarm optimization (MOPSO) is applied to search for the Pareto optimal solutions. The shape functions parameters and types in addition to the FGM power index are considered as the design variables. Several cases are studied to demonstrate the multiobjective optimal shape design of axially functionally graded beams.