Research On Method And Application Of BESO Based On Density Evolution

Evolutionary structural optimization (ESO) method has attracted widespread concern among researchers in topology optimization and practitioners in engineering since it was firstly introduced. The method is based on a concept that a structure evolves towards an optimum by gradually removing elements with least contribution to the optimization objective. Because of this simple concept, ESO method is easy to be implemented in existing commercial finite element analysis software to solve the problem of static, dynamic and many other optimization problems in engineering. With continuous development of the method, it also encounters many problems, such as local optimal solutions, numerical instabilities and so on. Many improvements in element removal criteria and algorithm process are made in this paper; the applicability in engineering cases of the modified method is also been discussed.Firstly, the influence of initial rejection ratio and evolutionary ratio on convergence of the optimization process is discussed. A performance index based on the discrete coefficient of stress is presented. Then an improved ESO method is presented, the major change is to calculate the evolutionary ratio of each iteration according to the ratio of performance index of the current iteration to the performance index of the first iteration. The new approach is demonstrated by solving the compliance minimization problem of a cantilever beam.Secondly, a new element removal and additional method is put forward based on analysis of reasons for the errors caused in sensitivity calculate. The step length of density evolution is reduced so that the accuracy of sensitivity analysis can be improved. A new material interpolation method is adopted to describe the relationship between the pseudo-density and the stiffness of gray elements. As a result of the bi-directional algorithm, the accidentally deleted elements could be recovered by density growth so that the improved method allows more thorough search of all the design space.Thirdly, the present work extends the ESO method to the stiffness optimization with a mass constraint, a max stress constraint and a local displacement constraint. The stress constraint and displacement constraint are replaced by a strain constraint according to the internal relation analysis among stress, displacement and strain. Then a simplified method for calculating strain sensitivity is proposed based on the displacement reciprocal theorem. A mixed weighted sensitivity method based on restrain judging is introduced to take constraint condition into account in the whole process of optimization so that it could be well satisfied. At the end of this chapter, an application program is developed on the platform of ANSYS, with which ESO method could be used to solve a variety of topology optimization problems in engineering applications.Finally, based on the research mentioned above, the modified ESO method is applied to the topology optimization of key parts of injection molding machines. Topology optimization examples of crosshead and molding board are presented to demonstrate the effectiveness of the proposed method and the application system.At the end of this paper, the main contents and achievements in this work are summarized, then the unsolved problems are pointed out and an outlook of the further research is presented.