Research On Structural Topology Optimization Design For Functionally Graded Materials

Functionally Graded Materials is a new kind of material with a gradient change of material properties. The structural topology optimization is to find the structural optimal topology configuration under the given boundary conditions. The application of Functionally Graded Material and structural topology optimization design are important approaches to the research of lightweight design. In this paper, the FGM structural topology optimization methods are researched for realizing two-dimensional & three-dimensional FGM structural topology optimization design in solving practical engineering problems, which have important practical significances in the lightweight design of the structure. Some details investigated in this paper are stated as follows.(1) Through linking design variables to material components, the FGM-SIMP material model is constructed. Combining with the gradient sensitivity function, the model for Variable Density Method is established, where the objective is to minimize compliance and the volume fraction is used as constraint condition.(2) By introducing the filter function, the FGM-ICM model is designed. Combining with the gradient displacement function, and considering displacement constraint, the approximate explicit model for ICM structural topology optimization of FGM is established. For solving the model, the filter method of linear atten uation is adopted to avoid checkerboards and mesh dependency problem. For obtaining clear topological configuration, the dynamic adjustment strategy for the topological variable threshold is proposed, and the optimization criterion based on the change rate of discreteness measure is used. The measure of discreteness is calculated for telling whether the optimized design is converged to a discrete solution. The results of numerical examples demonstrate that the proposed analysis method can effectively realize the structural topological optimization of FGM(3) Based on the ICM method, the multiple load-cases and the multi-load problems of FGM topology optimization are deeply studied. The model of FGM structure topological optimization under multiple load-conditions is established and resolved. Several numerical examples are optimized by the mothed, which verify the validity of the method proposed in this paper.