Multi-scale Structural Topology Optimization Based On Homogenization Method

Topology optimization has emerged as a vital tool for innovative structural design by optimizing the material distribution through mathematical calculation to achieve the optimal target performance.With the rapid advancement of advanced design concept and manufacturing technology,the structural topology optimization method for additive manufacturing has increasingly become the hot spot in the field of high-performance lightweight structure design,particularly for multi-scale structural topology optimization(MSTO)with porous microstructure filling.Compared to traditional single-scale solid structures,the novel multiscale design can achieve several remarkable mechanical properties,including high porosity,energy absorption,robustness,negative Poisson’s ratio,and ultimate anisotropy.However,the field of MSTO still faces numerous technical challenges,such as structural performance,computational efficiency,and microstructure connectivity.This paper comprehensively analyzes the research status of MSTO,summarizes the existing problems of several multi-scale structural design methods,and studies the MSTO design based on the homogenization method.Firstly,a novel lattice structure topology optimization(LSTO)method with extreme anisotropic lattice properties is proposed.While most of the candidate lattice structures for LSTO can only modify the microstructure gradient by altering lattice density or geometric parameters,which is evidently insufficient for addressing complex loading conditions within multi-scale structural components.To overcome this limitation,this study constructs candidate lattice structures with extreme anisotropy by combining pre-optimized basic lattice structures.The resulting candidate lattice structure exhibits excellent tensile modulus in the x-and ydirections,as well as shear modulus in the x-y plane.Furthermore,varying extreme anisotropic lattice properties changes are achieved with altering the composition of the candidate lattice structure,and the optimization design of multi-scale structures with excellent stiffness properties are validated by numerical examples and mechanical tests.Then,a multiscale topology optimization method for lattice-solid hybrid structures is proposed.Specifically,with introducing solid and void materials to extend the lattice structure material property,an ordered multi-phase material interpolation model is introduced,which enables the multi-parameter collaborative optimization of multiphase materials defined in the hybrid structure design.The proposed ordered multi-phase material interpolation model effectively avoids the occurrence of extremely high-density or low-density lattices,which is crucial for ensuring the compatibility of structural performance optimization and microstructure manufacturability to provides a promising solution.Later,a clustering-based topology optimization method for multi-scale structures is proposed.Specifically,the LSTO technique with multi-variable lattice structure parameters is introduced into the multi-scale design with free-form topological microstructures.A clustering optimization strategy is proposed,wherein the optimization results of the multi-variable LSTO are used as the macro-structure response characteristics to reflect the local bearing capacity level and principal stress state of the macro-structure.Multiscale topology optimization through the inverse homogenization approach is performed to further design the unit cell structures in each cluster.The proposed method is verified through typical topology optimization numerical examples and experimental tests,showing that the proposed method significantly improves the mechanical properties of multi-scale components,particularly compared with the clusteringbased optimization strategy with single structural response characteristics.Additionally,the proposed method ensures the interconnection of heterogeneous microstructures and exhibits good computational efficiency.Finally,the main work and innovations of this paper are summarized,and the future research is prospected.