Research On Multi-scale Topology Optimization Method For Manufacturable Lattice Structures

Lattice structures have the advantages of light weight and high performance,so it is widely applied in lightweight components,heat insulation,impact resistance and other fields.The topology optimization method is based on scientific theory,which can find the reasonable distribution of materials in the design domain realizing the optimal design of the structure providing a scientific basis and method for the lattice structure design.At present,most of researches on lattice structure topology optimization design is based on homogenization theory.But the scale separation hypothesis of homogenization theory causes connectivity issues and lack of explicit length ratios between macro-micro scale,which makes it difficult for lattice structure manufacture.Therefore,in practical engineering applications,the lattice structure design mostly stays in the stage of filling design,in which macrostructure and lattice unit are designed separately.However,the separation design of the macrostructure and the lattice unit does not consider the coupling relationship between the lattice unit and the macrostructure,making it difficult to fully exert its performance.Aiming at these problems,this paper proposes a multi-scale topology optimization method to achieve manufacturable lattice structure design.In the proposed method,design of single lattice unit or multi-structure lattice unit and macro structure is conducted simultaneously.The additive manufacturing of designed lattice structures is conducted to verify the manufacturability.The main works are as follows:Firstly,the sub-structure method based on static condensation is studied.The degrees of freedom of internal nodes of the substructure are statically condensed to form a superelement.In the super-element,the configuration of lattice units is defined and the stiffness matrix is calculated.Then the relationship between the design variables,lattice configuration and the stiffness matrix are established based on the proper orthogonal decomposition and parameter approximation,by doing this,the model of approximation of reduced substructure is built and the correlation between the lattice unit scale and the macro scale is realized.Secondly,a multi-scale topology optimization method for single-structured lattice structure is studied.At first,two types of lattice structure configuration are defined,and the scale correlation is performed by the method described above.Then the multi-scale topology optimization model of lattice structure is established based on the SIMP model,and the sensitivity analysis is carried out.The OC algorithm is used to solved the problem.Numerical examples are carried out to illustrate the effectiveness of proposed method.Thirdly,the multi-scale topology optimization method for multi-configuration lattice structure is studied.A new design variable is introduced to realize the continuous change of lattice unit configuration.The multi-scale topology optimization model of multiconfiguration lattice structure is also constructed based on SIMP model.The sensitivity analysis of two independent variables is conducted respectively,and the GCMMA algorithm is used to solve the problem.Numerical examples are carried out to illustrate the effectiveness of proposed method.Fourthly,the additive manufacturing of designed lattice structures is conducted and manufacturability is of the designed structures is verified.The simulation analysis and mechanical performance test show the consistency between the theoretical design results and the actual test results,and The effect of lattice unit configuration on structural properties is illustrated.Finally,the paper is summarized and future research directions are prospected based on the inadequacies of this thesis.