Research Of Topology Optimization Design Of Microstructure For Material Based On Homogenization Method

For the macro-mechanical properties of composite material are affected by the micro-structure and the parameters of material components, it's necessary and feasible to obtain composites with desired performance by the topology optimization design to the material micro-structure. Topology optimization design for microstructure of periodic material with the extreme elastic properties as optimization objective is studied on this paper.Based on the property prediction of periodic composites using homogenization theory, micro-structure topology optimization model with the extreme elastic properties is established. The SIMP is adopted in the model, by using the density of micro-unit as the design variable, the volume fraction of material as the optimization constraints, the macroscopic mechanical properties of material as the optimization objective, the OC method as the solution algorithm. The material micro-structure with optimal transverse tensile strength, optimal longitudinal tensile strength, optimal shear modulus and optimal weighted sums of bidirectional tensile strength are obtained.Several numerical instabilities phenomenon in micro-structure topology optimization process are described, and filtering of sensitivities technology is introduced to solve these problems. The influence of parameters in topology optimization model to optimal process and final optimization results is discussed. The results show that to increase the penalization factors, the optimization convergence process becomes faster. If filter radius is too small, the numerical instabilities such as checkerboard format cannot be completely eliminated, and while the value is too large the fuzzy boundaries will appear in the topology structure. The optimal parameters are chosen to construct an optimization model after analysis and comparison.Finally, the optimization model is applied to the hole shape design of aluminum alloy porous plate, obtaining a structure that the maximum potential of material is fully played at any working conditions. The obtained optimal structure effective bulk modulus are approach to upper limit value of Hashin-Shtrikman, which reveals the effective bulk modulus are interval stabile and the optimal results play obvious effects.In this paper, the micro-structure design of composites is carried out based on asymptotic homogenization theory and the theory of topology optimization. The implementation of the components with light weight and high strength is done.