| Structural design exists in various fields of practical engineering.Scientific and reasonable structure is an important guarantee for the safety,applicability,stability and durability of engineering projects.The empirical estimation and model test are applied in traditional structural design method to improve the design scheme.The purpose of design is only to meet the simple requirements of reliability.The design cycle of this product design pattern is long,the efficiency is low and it can’t guarantee the optimal design.In view of this problem,the theory of structural optimization design was born from it,which provides an efficient,scientific and reliable design tool for designers.In this paper,an adaptive step size bi-directional asymptotical structural optimization algorithm is proposed around the asymptotical structural optimization method,and a material interpolation model is proposed to improve the local modal problem for the simple harmonic response analysis method.Finally,based on the above research,the visual simulation system of structural topology optimization based on MATLAB is developed.The specific work is as follows:Firstly,based on the basic theory of finite element analysis,the flow of finite element analysis of three-dimensional continuum structure is deduced.The element code of some structures,the assembly mode of the overall stiffness matrix and the overall mass matrix in the process of finite element analysis are given.Then,combining the results of 3D continuum finite element analysis with the flow of bi-directional progressive structure optimization method,the program of the algorithm is compiled by MATLAB,which establishes the optimization model foundation for the subsequent dynamic topology optimization.Secondly,the evolutionary step size of the asymptotic structure optimization method is studied.Based on the controllable discrete coefficient,the adaptive step size bi-directional evolutionary structure optimization method is proposed.The method synthesizes the change trend of element sensitivity and volume constraints in the iterative process,and controls the evolution step length of structure by controlling the discrete coefficient,so as to effectively improve the solution speed of the algorithm.At the same time,for the topology optimization problem that the initial structure volume is smaller than the volume constraint variable,the reason of oscillation is analyzed,and the corresponding two-way progressive topology optimization process is proposed.The effectiveness of this method is verified by an optimization example.Then,the application of bi-directional asymptotic structure optimization method in dynamic optimization is studied.The advantages and disadvantages of different simple harmonic response solution methods are analyzed,and the sensitivity formulas under different solution methods are derived.The reason of local modal phenomenon caused by simp material interpolation model is explained in detail,and the advantages and disadvantages of different material interpolation models in modal analysis are compared horizontally.On this basis,the corresponding material interpolation model is proposed to improve the accuracy of the dynamic response analysis method,and the effectiveness of the material interpolation model is verified by an optimization example..Finally,the user interface of structure topology optimization is developed by MATLAB software.The system realizes the dynamic(static)response optimization of topology optimization of 3D continuum structure,and can export the optimization results to generate 3D printing files.Using visual means,the applicability and operability of bi-directional asymptotic structure optimization algorithm can be improved,and the feasibility of the system through numerical examples is verified. |
