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The present work applies meta-heuristic multi-objective particle swarm optimization (MOPSO) and non-dominated sorting genetic algorithm (NSGA)-II algorithms to predict optimal shape and material distribution of two-directional functionally graded tapered (2DFG-T) microbeams. The cross-section of the microbeam changes linearly along its length in both height and width directions. The rates of these changes are taken as the geometric design variables. Rather than the simple power law, two different trigonometric functions are introduced to provide various effective and flexible 2D- distributions of metal and ceramic phases. Using Hamilton's principle, the mathematical model is derived based on the third order shear deformation theory (TSDT) and modified couple stress theory (MCST). Developing a computationally efficient and time saving semi-analytical approach, the governing set of variable-coefficients partial differential equations is solved for the frequency and critical buckling under different boundary conditions. Several constrained single- and multi-objective optimization problems are formulated and solved to determine optimal material and geometry parameters of 2DFG-T microbeams to achieve maximization of fundamental frequency and/or critical buckling load while minimizing the structural mass. Various optimization results demonstrate that including shape parameters in addition to material distribution parameters as design variables results in more economical and flexible profiles that is critical for the manufacture of 2DFG-T microbeams. The following model can be exploited in the optimum design of FG microscale nanobeams including their shapes and material distribution. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]