Topology Optimization Of Continuum Structure Based On The Method Of Moving Asymptotes

This thesis mainly studies the topology optimization problem of continuum structure with minimum weight requirements under displacement constraints, which is based on the method of the moving asymptotes and a design space adjustment approach.Firstly, for the structural topology optimization minimum weight problem with the displacement constraint, using the method of moving asymptotes and combining the idea of the Independent, Continuous and Mapping method, a set of approximate displacement expressions that is suitable for large range of design variables is derived. And combining the approach of variable displacement limits with dual programming, a kind of high efficiency structural topological optimization design method is formed. By using this method, the oscillating phenomenon of objective function in the Independent, Continuous and Mapping method is solved, on the other hand, computation efficiency of optimization iteration is improved; Secondly, in order to decrease the solving error caused by using heuristic rules, and further improve the computation accuracy and efficiency of optimization designs, a kind of topological optimization design method based on the method of generalized moving asymptotes (GMMA) is proposed. Thirdly, in order to escape the local solution by adopting the rational fractions material model, the relationship between the structure stiffness and topological variables is established, meanwhile, a space design adjusting method which does not affect the convergence property of the smooth algorithms is given. Then, a set of explicit approximate expansions for displacement constraint functions based on the pour design variables and the method of moving asymptotes is obtained. Moreover, the element deletion and adding criterion and a set of structural optimization strategies are given, and a new kind of topology optimization method for continuum structure is established.For the methods mentioned above, their procedures are implementted, and a lot of typical structural design examples are given, and the obtained results show that the proposed methods in this thesis are correct and efficient, and are of good engineering application value.