Design optimization of functionally graded plates under thermo-mechanical loadings to minimize stress, deformation and mass

Abstract

This work addresses the multiobjective design optimization of metal-ceramic functionally graded (FG) plates, which are composed of a main functionally graded material (FGM) layer and may include metal and/or ceramic faces, under thermo-mechanical loadings. The design variables are the thickness of the FGM layer, the index of its power-law distribution of metal-ceramic volume fractions, and if included, the thickness of the metal and/or ceramic faces. The three objectives focus on mass, maximum transverse displacement and maximum value of the Tsai-Hill failure criteria to measure the stress field, aiming to minimize all together. Both thermal and mechanical problems are solved simultaneously using a layerwise mixed model based on least-squares formulation with multi-field independent variables, namely, displacements, temperature, transverse stresses, transverse heat flux, in-plane strains and in-plane components of the thermal gradient. The FGM layer z-continuous effective properties are fully described via high-order z-expansions, similarly to finite element approximations. The multiobjective optimization problem is solved by Direct MultiSearch (DMS) derivative-free method, which uses the notion of Pareto dominance to retain a list of feasible non-dominated solutions. Numerical results provide optimal designs of FG plates under thermo-mechanical loadings, exploring distinct metal-ceramic constituent materials and different side-to-thickness ratios, including three-dimensional approximate solutions for validation.