Thermomechanically coupled sensitivity analysis and design optimization of functionally graded materials

This paper presents a systematic numerical technique for performing sensitivity analysis of coupled thermomechanical problem of functionally graded materials (FGMs). General formulations are presented based on finite element model by using the direct method and the adjoint method. In the modeling of spatial variances of material properties, the graded finite element method is employed to conduct the heat transfer analysis and structural analysis and their sensitivity analysis. The design variables are the volume fractions of FGMs constituents and structural shape parameters. The design optimization model is then constructed and solved by the sequential linear programming (SLP). Numerical examples are presented to demonstrate the accuracy and the applicability of the present method.