基于移动粒子法的连续体结构拓扑优化研究

发布时间：2018-05-03 01:21

本文选题：移动粒子法 + 移动步长　；参考：《湘潭大学》2011年硕士论文

【摘要】：拓扑优化作为结构优化的概念设计阶段,是当前结构优化领域的热门研究课题之一,尽管大量学者对拓扑优化方法进行了深入的研究,但目前都采用“删除”节点得到拓扑优化结果。本文基于无网格伽辽金法,通过优化准则法得到节点密度并构造密度梯度算子,提出了一种新型的拓扑优化方法——移动粒子法,并对二维连续体结构进行了研究,主要研究内容如下: 1.针对目前多数拓扑优化方法由于采用“删除”单元或节点得到拓扑优化结果而常出现一些数值不稳定性现象,提出了通过“移动”节点得到拓扑优化结果来解决这些问题的方法。 2.通过采用各向同性惩罚插值模型及变密度法,建立以节点密度及其坐标位置为设计变量,柔度为目标函数的移动粒子法二维连续体结构拓扑优化模型;通过节点密度及优化准则法构造密度梯度算子及粒子移动控制方程,得到设计变量的迭代格式,并确定移动粒子法的背景网格的积分方案。通过FORTRAN软件编写相关程序对算例进行分析计算,证实了将移动粒子法应用于拓扑优化领域的可行性及优越性。 3.针对移动步长对拓扑优化结果有较大影响这一现象进行了讨论,得出最佳移动步长大小,使其在保证结果质量的同时迭代步数最少。 4.针对移动粒子法由于粒子堆积、迭代步数多等原因在拓扑优化过程中造成的刚度矩阵奇异、计算时间长等问题,提出了两种改进方案。通过算例结果表明中心点移动法可以缓解但不能完全消除粒子在边界处聚集,同时未能减少迭代步数;而变移动步长区域插点法可以完全消除边界粒子堆积现象并能向结构内部渗透,同时可以减少将近一半的迭代次数,其改进效果更好。本文成功实现了通过移动节点位置来得到拓扑优化结果这一构想,同时改进了移动算法,成功消除了迭代过程中出现的粒子堆积及计算时间长等问题。这一研究充分发挥了无网格法的优势,为拓扑优化方法的研究提供了新的思路。
[Abstract]:As one of the most popular research topics in the field of structural optimization, topology optimization is one of the most popular research topics in the field of structural optimization. Although a large number of scholars have studied the topology optimization methods in depth, the topology optimization results are obtained by "deleting" nodes. This paper is based on the meshless Galerkin method and obtains the nodes through the optimization criterion method. The density and density gradient operator is constructed, and a new topology optimization method, mobile particle method, is proposed, and the structure of two-dimensional continuum is studied. The main contents are as follows:
1. for most of the current topology optimization methods often appear some numerical instability due to the use of "delete" unit or node to get topology optimization results, and propose a method to solve these problems by using "mobile" node to get topology optimization results.
2. by using the isotropic penalty interpolation model and the variable density method, the topology optimization model of two dimensional continuum structure is set up with the node density and its coordinate position as the design variable and the flexibility is the target function. The density gradient operator and the particle movement control equation are constructed by the node density and optimization criterion method. The iterative scheme of the quantity and the integral scheme of the background grid of the mobile particle method are determined. The related programs are compiled by FORTRAN software to analyze and calculate the examples. The feasibility and superiority of applying the mobile particle method to the topology optimization field are proved.
3. the effect of the moving step on the result of topology optimization is discussed, and the best moving step size is obtained to ensure the least iteration step while guaranteeing the quality of the result.
4. to solve the problem of the stiffness matrix singularity and the long calculation time caused by the accumulation of particles and the number of iterative steps in the mobile particle method, two improved schemes are proposed. The results show that the center point movement method can be relieved but not completely eliminate the aggregation of the particles at the boundary, and can not reduce the iteration step. The variable moving step area interpolation method can completely eliminate the phenomenon of boundary particle accumulation and penetrate into the structure, and can reduce the number of iterations by nearly half, and its improvement effect is better.
In this paper, the concept of topology optimization is achieved through the location of mobile nodes. At the same time, the mobile algorithm is improved, and the problems of particle accumulation and long calculation time are eliminated successfully. This study gives full play to the advantages of the meshless method and provides a new way of thinking for the study of the extension method.

【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2011
【分类号】：TH122

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