基于Von Mises应力的ESO方法有效性研究

发布时间：2018-04-07 19:03

本文选题：渐进结构优化　切入点：Von　出处：《重庆大学》2012年硕士论文

【摘要】：机械产品的设计将经历一个从总体框架设计到细节结构优化设计的过程，结构优化设计始于拓扑优化，一个优良的拓扑能够为后续进行的形状和尺寸优化指明正确的方向。近二十年来，渐进结构优化方法（ESO）在结构拓扑优化领域中扮演着重要的角色，该理论方法的发展和完善引起了众多研究者的关注。虽然渐进结构优化算法在理论研究和工程应用方面都取得众多研究成果，但是该算法被认为是一种启发式算法，缺乏严格的数学理论基础。基于Von Mises应力准则的ESO的目标函数与优化准则之间模糊的关系至今未能用合理的显函数来表示；设计变量的离散特性被视为破坏了目标函数和约束函数的连续性和可微性；删除率和进化率等优化参数依靠经验取值的做法让算法的可靠性和通用性饱受质疑；算例结果与Michell桁架结构作粗略对比的验证手段比较缺乏说服力。本文就ESO方法有效性问题，，以解析法推导出基于VonMises应力的满应力准则下的长悬臂式、短悬臂式以及槽型约束边界式等几种静定结构的最优拓扑和形状，为验证结果是否为最优解提供了数学依据；基于ESO算法的思想，分析了几种不同边界条件的桁架结构和连续体结构的拓扑优化过程；以基于Von Mises应力准则的ESO算法的四条基本假设作为分析对象，从满应力与最小体积、VonMises应力与材料效率、渐进方法的必要性及其效率、离散变量与连续变量的优化解法等方面对ESO方法的有效性进行了研究；本文研究从实例验证方面并在一定程度上从理论方面证明了ESO方法具有很好的寻优能力。结构拓扑优化设计往往在得出比较粗略的结构后就终止，只关注最主要的承载结构，而忽视了在承载结构间的孔洞区域内合理布置更细节的拓扑结构的重要性。BESO对单元的恢复往往只能够沿着存活单元边界进行，很难在孔洞区域架起新的支承结构。本文基于ESO方法和变密度法提出了二次删除策略以对现有ESO方法进行改进，该算法可在孔洞区域进行二次或者多次优化，具有更好的全局寻优能力，并通过一个经典的简支梁算例验证了该方法的可行性。
[Abstract]:The design of mechanical products will go through a process from the overall frame design to the detailed structure optimization design. The structural optimization design begins with the topology optimization. A good topology can point out the correct direction for the subsequent shape and size optimization.In the past two decades, the evolutionary structural optimization method (ESO) has played an important role in the field of structural topology optimization. The development and improvement of this theoretical method has attracted many researchers' attention.Although the asymptotic structural optimization algorithm has made many achievements in both theoretical research and engineering application, it is considered to be a heuristic algorithm and lacks a strict mathematical theoretical basis.The fuzzy relation between the objective function and the optimization criterion of ESO based on Von Mises stress criterion has not been represented by reasonable explicit function, and the discrete characteristic of design variables is regarded as destroying the continuity and differentiability of objective function and constraint function.The reliability and generality of the algorithm are questioned by the method of empirical selection of the optimization parameters such as deletion rate and evolution rate, and the comparison between the results of the numerical examples and that of Michell truss structures is not convincing.In this paper, the optimal topologies and shapes of several statically indeterminate structures, such as long cantilever, short cantilever and groove-constrained boundary type, are derived by analytical method for the validity of ESO method under the full stress criterion of VonMises stress.Based on the idea of ESO algorithm, the topological optimization process of truss structure and continuum structure with different boundary conditions is analyzed.Taking four basic assumptions of ESO algorithm based on Von Mises stress criterion as analysis object, the necessity and efficiency of progressive method are analyzed from full stress and minimum volume Von Mises stress and material efficiency.In this paper, the validity of ESO method is studied in terms of the optimization method of discrete variables and continuous variables. In this paper, the effectiveness of ESO method is proved to be very good in the aspect of example verification and, to a certain extent, the theoretical aspect.Structural topology optimization design often ends after the relatively rough structure, and only focuses on the most important bearing structure.The importance of reasonable arrangement of more detailed topological structures in the voids between load-bearing structures is neglected. The restoration of the elements by BESO can only be carried out along the boundary of the surviving units, and it is difficult to set up new supporting structures in the voids.Based on the ESO method and the variable density method, this paper proposes a quadratic deletion strategy to improve the existing ESO method. The algorithm can be optimized twice or multiple times in the hole region, and has better global optimization ability.The feasibility of the method is verified by a classical simply supported beam example.
【学位授予单位】：重庆大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TH122

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