Research On BESO Topology Optimization Method Based On Dynamic Evolution Rate And Self-adaptive Mesh

Topology optimization is an important branch of structural optimization,and it has a very broad engineering application prospect.Bi-directional Evolutionary Optimization(Bi-directional Evolutionary Optimization,BESO)is one of the current mainstream topology optimization methods because it has no gray-scale unit problem and is easy to be combined with commercial finite element software.The BESO method has gradually obtained a series of improvements since its introduction,but there are still problems such as low optimization calculation efficiency,long time consumption,severe grid dependence,and severe boundary aliasing.In response to the above problems,the basic principle of the BESO method in this paper proposes two major improvements to the BESO: the dynamic evolution rate strategy and the adaptive grid method,which can not only greatly improve the optimization calculation efficiency,shorten the convergence time of the algorithm,but also effectively Solve the problems of traditional grid dependence and serious border aliasing.The main work and innovations are as follows:(1)First aspect: The traditional two-way progressive structure topology optimization method generally adopts a constant evolution rate.If a larger evolution rate is adopted,it may cause a deviation of the evolution direction or unstable convergence.On the contrary,if a smaller evolution rate is adopted,it will lead to a slow evolution rate and low calculation efficiency.This paper introduces two types of S-curve functions based on Arctangent and Logistic.By adopting the dynamic change idea of "fast first and slow second" to improve the problem of low evolution rate of traditional methods,a BESO method based on dynamic evolution rate strategy is proposed.,Which is the DER-BESO method.This method guarantees the rapid evolution of the structural topology with a high evolution rate in the early stage of topology optimization,and automatically switches to a low evolution rate in the later stage of topology optimization to ensure the stability of convergence.Tests on typical examples show that the DER-BESO method based on Arctangent requires only 40% to 50% of the iteration steps of the conventional BESO method,and the DER-BESO method based on Logistic requires only the iteration steps of the conventional BESO method.From 50% to 60%,the calculation efficiency has been greatly improved.(2)The second aspect: the traditional BESO method is very dependent on the grid,which is mainly reflected in the grid division of different thicknesses often affecting the final optimization design results.Although in theory the grid can be subdivided as close as possible to approximate the continuum to improve the smoothness of the boundary,the subdivision grid will greatly increase the calculation amount of the finite element analysis for each iteration step,and the calculation time will be exponential with the grid density Level growth.Therefore,this paper introduces a quad / octree algorithm to build an adaptive grid,and adjusts the thickness of the local grid of the structure in the topology optimization process to solve the above problems,in order to further improve the calculation efficiency and obtain a smoother structural boundary.Finally,for the BESO method based on the dynamic evolution rate and adaptive grid proposed above,this paper uses the improved algorithm written by the secondary development programming language APDL of the commercial finite element analysis software ANSYS,combined with ANSYS powerful finite element solver,It can easily realize topological optimization of complex two-dimensional and three-dimensional structures.