Topology Optimization Of Column-disk Structure And Its Realization In MATLAB

At present,the structure optimization has already become the key point of the industrial design research.Because it is an effective way which can improve the service life of the parts,shorten the design period,reduce the manufacturing cost and the energy consumption in the project.Topology optimization,as one of the most promising levels in structural optimization,has become one of the hottest subjects in the optimization research's field in these years.Compared with the traditional optimization design,topology optimization design does not rely on the experience of designers and can obtain the optimal distribution of materials on the basis of improving or maintaining the structure performance.Topology optimization design makes it possible for complex structures to optimize their schemes reasonably and quickly in the conceptual design stage.As the main theoretical algorithm of topology optimization design,variable density method is widely used to realize lightweight design of construction machinery and other parts.The study of its theory and the improvement of its shortcomings have always been the research hotspot of many scholars.This paper based on the finite element analysis,variable density method was used to optimize the structure of the column-disk topology design and the optimization process is programmed with the MATLAB software.Before all others,this paper make a brief description about the status of research and problems of topology optimization theory and algorithm at home and abroad.The paper also described the development and current situation of topology optimization research that based on MATLAB.And the necessity and feasibility of using MATLAB to optimize the topology of cylinder-disk structure that based on variable density method are proposed.Next in important,this paper expounded the basic concept,design level and classification of structural optimization problem.Make researches of the concepts and characteristics of size optimization,shape optimization and topology optimization.The basic theory,principle,advantages and disadvantages of the optimization algorithms for topology optimization are also studied,these studies including homogenization method,variable thickness method,level set method,variable density method and asymptotic structure optimization method In this paper,the mathematical programming method,heuristic algorithm and optimization criterion method used in topology optimization calculation are analyzed.Make a preparation for the theory and algorithm of topology optimization.Then,the paper studied the basic theory and design flow of finite element analysis,and the finite element model of column-disk structure is established according to the procedure.In the first step,the influence of grid element type and grid density on the optimization results is analyzed,and the mesh partition of four-node tetrahedral element with column-disk structure is realized.Then the stiffness matrix of the four-node tetrahedral element is solved and the constrained load is applied to the optimized structure.In addition,by comparing SIMP material interpolation model with RAMP material interpolation model,the study discovered the effect of penalty factor on penalty effect is studied.And in this paper,four kinds of numerical instability in topology optimization are analyzed and the corresponding strategies are come up with.The filter function is introduced into the SIMP model to avoid the checkerboard lattice,grid dependence and local extremum problems.The result is that a topology optimization mathematical model is set up.Then,the effects of different penalty factors p,filter radius r_min and volume ratio v on the topology optimization results were analyzed by examples.In the last part of the paper,on the basis of variable density method,the basic flow of topology optimization can be found.The topology optimization process of cylindrical disk structure is programmed with MATLAB software,and the results of topology optimization are obtained.And some examples of topology optimization of column-disk structure under different loads are given.