Simple Continuum Structure Based On Level Set Method Research On Dynamic Topology Optimization

Structural optimization is to find the best design solution according to certain goals under given constraints.In structural optimization methods,topology optimization has superior flexibility and diversity than size and shape optimization.Therefore,topology optimization methods have become the main research direction in the field of structural optimization design.The level set topology optimization method based on the reaction-diffusion equation can not only achieve the optimization of the size and shape of the structure at the same time,but also control the complexity of the topology structure through regularization parameters,and suppress numerical problems such as checkerboards and gray cells.Based on the level set topology optimization method based on the reaction-diffusion equation,this paper studied dynamic optimization problems,multi-constrained optimization problems,and periodic multi-material optimization problems.Firstly,the dynamic response of the structure and the calculation of the objective function are tedious and complicated during the dynamic topology optimization iteration.The equivalent static load method is combined with the level set topology optimization method.Constructing a mathematical model for dynamic topology optimization of the structure using the level set method can not only efficiently and quickly solve the dynamic response and objective function of the structure,but also realize the transformation of dynamic and static topology optimization.Secondly,in order to solve the problem that the performance of the topology optimization model that can only achieve lightweight can no longer meet the actual requirements of engineering,the dynamic topology optimization method of level set is combined with the multi-constrained optimization problem.Construct the level set method of structural dynamic topology optimization mathematical model with constraints of interest,Von Mises stress,and structural distortion energy as constraints.By setting appropriate allowable displacement,allowable stress and allowable distortion energy,the topological structure with reliable stiffness and strength can be obtained.Finally,based on the dynamic topology optimization method of level set,the dynamic topology optimization research of periodic multi-material structures is carried out.Two kinds of periodic multi-material topology optimization methods based on Von Mises stress are proposed.According to the element stress range,the material is redistributed in the cells divided into different periodic sub-intervals to obtain high-performance,periodic multi-material topology.