Research On Three Dimensional Multimaterials Structure Topology Optimization Based On The Improved Level Set Method

The purpose of structural topology optimization is to find the best force transmission path in the structure,reduce the weight of the structure and the cost of materials after meeting the requirements of structural design.Structural topology optimization has became the research hotspot in the field of structural optimization because of it can assist the structural design and provide the inspiration for the determination of the design scheme.Besides,the level set topology optimization method solved by the reaction-diffusion equation can simultaneously achieve the shape and topological optimization of the structure,and it can effectively avoid the occurrence of numerical phenomena such as checkerboard.In this paper,some improvements and theoretical researches on the three-dimensional structural optimization and multi-material structural optimization of level set topology optimization solved by the reaction diffusion equation were carried out.The following works were researched in this paper:First of all,the relevant improvement research on level set topology optimization method based on the theory of level set function was carried out.On the one hand,the reasons that level set topology optimization method may not converge in volume constraints when solving some models were analyzed.So that two measures to make the volume constraint converges were proposed by controlling the Lagrange multipliers.On the other hand,some improved methods to increase solve efficiency of level set topology optimization method was proposed.Secondly,the topological derivative of 3D structure was derived,and then the solving model of 3D structural topology optimization based on the level set method was established,which can be used to realize topology optimization of three-dimensional structure.Finally,in order to achieve the full use of materials in the structure,reduce the cost of materials,the level set topology optimization method was used to solve the multi-material topological optimization problem of two and three-dimensional structures in which a multi-material structure topology optimization model based on the maximization of structural stiffness as objective function and the placement stability of element material as the convergence condition was established.The material in the design area can be fully utilized by reasonably setting the element stress range of the element material.Two kinds of elementstress introduction modes were designed;the multi-material structure topology optimization with different requirements was realized.