Material and shape optimization of bi-directional functionally graded plates by GIGA and an improved multi-objective particle swarm optimization algorithm

In the design of functionally graded materials, bi-directional design offers greater design freedom than the typical single-direction approach. This paper studies the shape and size design of variable-thickness bi-directional functionally graded plates (2D-FGPs) with multi-objective optimization. A method integrating generalized iso-geometrical analysis (GIGA) and an improved multi-objective particle swarm optimization algorithm (IMOPSO) is proposed, with numerous technical advantages. B-spline basis functions in two dimensions are used to robustly represent the volume fraction distribution, with volume fraction and shape profile at control points located along the plane set to be design variables. The mechanical behavior of the 2D-FGPs is treated with a third-order shear deformation theory and a non-uniform rational basis spline (NURBS)-based GIGA scheme. The IMOPSO algorithm incorporates chaotic sequence mapping, a diversity feedback mechanism, and a hybrid mutation mechanism to mitigate premature convergence and enhance evolution of the Pareto frontier. A number of test examples are provided, on square, circular, and gear FGPs with various loading configurations, optimizing for natural frequency and mass. (C) 2020 Elsevier B.V. All rights reserved.