基于变密度法的连续体结构拓扑优化

发布时间：2018-01-29 22:00

本文关键词： 拓扑优化变密度法惩罚函数多工况　出处：《东北大学》2014年硕士论文　论文类型：学位论文

【摘要】：结构的拓扑优化技术能够在给定载荷及约束条件下,寻找到使结构设计目标最优化的材料密度分布,让设计的结构利用材料更经济、受力分布更合理,从而带来显著的经济效益。结构拓扑的改进可以极大的改善结构性能或减轻结构重量,成为近年来国内外研究热点。拓扑优化是产品的创新性概念设计阶段,尽管经过研究人员的不懈努力,这一领域的研究已经取得了很大的进展,但仍存在一些问题值得进一步深入探讨。本文的研究对象是连续体结构,分别就拓扑优化的基本理论和方法、优化中参数的影响、基于变密度法的拓扑优化准则算法及密度差值函数等方面进行了比较深入的研究。论文的主要研究工作：1、利用HyperWorks软件对拓扑优化过程中的优化参数对优化结果的影响进行详细的分析与研究,得出优化参数对于优化结果影响的一般规律。并结合参数的影响,探讨拓扑优化中出现数值不稳定现象的原因。2、通过工程实例,对不同工况下的结构进行拓扑优化,详细分析不同工况对于优化结果的影响,并通过对比不同材料下的拓扑优化结果,验证了轻量化的另一途径——轻质材料。3、在研究三种工程中应用较多的材料密度插值模型：SIMP、RAMP、Sigmoid。的基础上,根据密度插值法理论和拓扑优化准则,依托SIMP和Sigmoid函数,创建了S-S密度差值函数,推导出相应的数学公式,通过典型的例子验证了S-S法的可行性和有效性。
[Abstract]:The topology optimization technology of structure can find out the material density distribution which can optimize the structure design objective under the given load and constraint conditions, make the structure use the material more economically, and the force distribution is more reasonable. The improvement of structure topology can greatly improve the structure performance or reduce the weight of the structure, which has become a hot research topic at home and abroad in recent years. Topology optimization is the stage of innovative conceptual design of products. Although great progress has been made in this field through the unremitting efforts of the researchers, there are still some problems that need to be further discussed. The object of this paper is continuum structure. The basic theory and method of topology optimization and the influence of parameters in optimization are discussed respectively. The topology optimization criterion algorithm based on variable density method and density difference function are studied deeply. The main work of this paper is: 1. HyperWorks software is used to analyze and study the influence of optimization parameters on the optimization results in the process of topology optimization in detail. The general law of the influence of optimization parameters on optimization results is obtained. Combined with the influence of parameters, the cause of numerical instability in topology optimization is discussed. Topology optimization of structures under different working conditions is carried out, and the effects of different working conditions on optimization results are analyzed in detail, and the results of topology optimization under different materials are compared. Another way of lightweight, light weight material. 3, is verified, which is based on the research of the material density interpolation model: SIMP / Ramp Sigmoid. which is widely used in three kinds of projects. According to density interpolation theory and topological optimization criterion, S-S density difference function is established by relying on SIMP and Sigmoid functions, and the corresponding mathematical formula is derived. The feasibility and effectiveness of S-S method are verified by typical examples.
【学位授予单位】：东北大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TB114

【相似文献】