自适应伽辽金法在结构拓扑优化中的进一步研究

发布时间：2018-01-02 05:26

本文关键词：自适应伽辽金法在结构拓扑优化中的进一步研究　出处：《湘潭大学》2012年硕士论文　论文类型：学位论文

【摘要】：结构拓扑优化兴起于20世纪初，作为一种新型设计方法，它是优化技术中最具希望和吸引力的课题。而基于无网格法的拓扑优化只需利用点将问题域离散，没有单元束缚，计算精度高，但仍存在计算不稳定、效率低等不足。本文的自适应加密技术正是为提高计算效率而做的研究。本文系统地介绍了无网格伽辽金法的基本理论，以经典的铁木辛柯梁为对象，将伽辽金法与有限元法进行比较。同时，探讨不同的几种权函数对形函数的影响，并研究了背景网格的布置与节点排布间的关系。确定了h型中卫加密与卫卫加密相结合的自适应加密方案。在变密度法的基础上，运用伽辽金法，构建连续体优化的物理模型与数学模型。对SIMP和RAMP两种插值模型分别推导了目标函数计算公式，并通过两个悬臂梁算例对这两种模型作出比较分析。针对优化中的棋盘格式等数值不稳定性问题，总结了相应的解决办法，并结合算例应用改进的过滤技术，提高了计算效率。基于无网格法和拓扑优化理论，探讨比较了不同节点布置、不同背景网格对优化结果的影响，提出应用自适应技术需要注意的两个问题。在伽辽金法的拓扑优化基础上，以L形梁、T形梁为对象，研究了在二维连续体结构拓扑优化中应用自适应加密技术的内容，实现了改善计算效率的目标，并将结果与未应用加密技术的结果进行计算效率的对比，使自适应加密技术的优势得以验证。与此同时还讨论了不同疏密程度下，，初始节点分布带来的不同优化结果。本文主要计算工作都通过在MATLAB软件中编写程序得以实现。研究表明在基于无网格法的结构拓扑优化问题中，融入自适应加密技术可提高优化效率。自适应技术与无网格法的联合应用是结构优化的一个亮点，潜力巨大。
[Abstract]:As a new design method, structural topology optimization is one of the most promising and attractive topics in optimization technology, and topology optimization based on meshless method only needs to use points to discretize the problem domain. There is no element binding and high accuracy, but there are still some shortcomings such as unstable calculation and low efficiency. The adaptive encryption technique in this paper is just to improve the computational efficiency. In this paper, the basic theory of the meshless Galerkin method is introduced systematically. The Galerkin method and the finite element method are compared with the classical Temocco beam. This paper discusses the influence of different weight functions on shape functions, studies the relationship between background grid arrangement and node arrangement, and determines an adaptive encryption scheme which combines h type central guard encryption with security encryption. On the basis of variable density method, the physical model and mathematical model of continuum optimization are constructed by Galerkin method. The objective function formulas for SIMP and RAMP interpolation models are derived respectively. The two models are compared and analyzed by two cantilever beam examples. Aiming at the numerical instability problems such as the chessboard format in the optimization, the corresponding solutions are summarized, and the improved filtering technology is applied in combination with the example. The calculation efficiency is improved. Based on meshless method and topology optimization theory, the effects of different nodes layout and different background meshes on the optimization results are discussed and compared. Based on the topology optimization of Galerkin method, the L-shaped beam and T-shaped beam are taken as the object. The content of adaptive encryption technique in topology optimization of two-dimensional continuum structure is studied. The goal of improving computing efficiency is realized, and the result is compared with the result without encryption technology. The advantages of adaptive encryption are verified. At the same time, different optimization results of initial node distribution are discussed under different degree of density. The main calculation work of this paper is realized by programming in MATLAB software. The research shows that in the structure topology optimization problem based on meshless method. The combination of adaptive encryption and meshless method is a bright spot in structural optimization and has great potential.
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TH122

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