This paper presents a multiscale design method for simultaneous topology optimization of both macrostructures and microstructures.Geometric features are extended as design primitives at both macro and micro scales and...This paper presents a multiscale design method for simultaneous topology optimization of both macrostructures and microstructures.Geometric features are extended as design primitives at both macro and micro scales and represented by Level Set Functions(LSFs).Parameters related to the locations,sizes,and orientations of macro and micro features are considered as design variables and optimized simultaneously.In the overlapping areas of different macro features,embedded microstructures are optimally figured out as the solution of the corresponding sub-optimization,problem.In this study,the eXtended Finite Element Method(XFEM)is implemented for structural and sensitivity analyses with respect to design variables.This method has the advantage of using a fixed grid independent of the topology optimization process.The homogenization procedure is applied to calculate the effective properties of considered microstructures in each macro feature.Numerical examples are presented to illustrate the effectiveness of the proposed method.Results depict that the multiscale design cannot obviously improve structural stiffness compared with a solid-material design under the linear elastic condition.展开更多
基金supported by National Key Research and Development Program of China(No.2017YFB1102800)National Natural Science Foundation of China(Nos.11432011,11620101002,11722219).
文摘This paper presents a multiscale design method for simultaneous topology optimization of both macrostructures and microstructures.Geometric features are extended as design primitives at both macro and micro scales and represented by Level Set Functions(LSFs).Parameters related to the locations,sizes,and orientations of macro and micro features are considered as design variables and optimized simultaneously.In the overlapping areas of different macro features,embedded microstructures are optimally figured out as the solution of the corresponding sub-optimization,problem.In this study,the eXtended Finite Element Method(XFEM)is implemented for structural and sensitivity analyses with respect to design variables.This method has the advantage of using a fixed grid independent of the topology optimization process.The homogenization procedure is applied to calculate the effective properties of considered microstructures in each macro feature.Numerical examples are presented to illustrate the effectiveness of the proposed method.Results depict that the multiscale design cannot obviously improve structural stiffness compared with a solid-material design under the linear elastic condition.
