移动粒子法拓扑优化效率影响因素的研究
发布时间：2018-11-18 14:50
【摘要】：作为一种新型的结构拓扑优化方法，，移动粒子法成功地消除了优化过程中出现的一些数值不稳定现象。但是与其他类型的拓扑优化方法相同，移动粒子法也存在着计算耗时长、优化求解效率低等问题，这也制约了其在工程实际中的应用。本文主要从本质边界条件的处理方式与移动步长大小的确定方法两方面研究了拓扑优化效率的影响因素，在此基础上提出运用位移约束方程法施加本质边界条件并利用自适应移动步长插点法进行拓扑优化，主要研究内容如下： 1.分析了无网格Galerkin法结构分析时本质边界条件的处理方法对计算效率的影响；提出运用位移约束方程法施加本质边界条件，阐述了位移约束方程法的基本理论。利用Visual Fortran编程分析了相关算例，结果表明位移约束方程法在保证计算结果精度的前提下可以提高计算效率并能够节省存储量。 2.对比了拉格朗日乘子法与位移约束方程法在拓扑优化时的效率，进一步证实了位移约束方程法在提高拓扑优化效率方面的优势；分析了移动粒子法节点最小密度值出现退化的原因，提出了自适应移动步长插点法。通过Visual Fortran编写程序对相关算例进行了分析讨论，验证了该方法在提高拓扑优化求解效率方面的优势。 3.针对可移动节点密度判定值这一重要参数对拓扑优化结果及优化效率的影响进行了分析讨论；得到了可移动节点密度判定值的大小与迭代次数及最终拓扑边界连续性的相互关系，为改进优化算法的提出提供了一个突破口。 4.分析了自适应移动步长插点法在计算节点最小密度值小于0.1时迭代次数多、耗时长的原因；结合可移动节点密度判定值对优化迭代过程的影响，提出了一种改进的优化算法。利用Visual Fortran编程将其实现，算例分析结果表明，改进的优化算法缩短了节点最小密度值小于0.1的迭代次数与计算时间，提高了拓扑优化效率。 本文运用位移约束方程法处理本质边界条件，并利用自适应移动步长插点法进行拓扑优化，成功地消除了在迭代过程中出现的节点最小密度值及其梯度值退化现象。在前面分析基础上提出的改进优化算法，缩短了节点最小密度值小于0.1时的计算时间，在保证计算结果质量的同时，进一步提高了拓扑优化效率。
[Abstract]:As a new topology optimization method, moving particle method successfully eliminates some numerical instability in the optimization process. However, as with other topology optimization methods, the moving particle method also has the problems of long calculation time and low efficiency, which restricts its application in engineering practice. In this paper, the factors affecting the efficiency of topology optimization are studied from two aspects: the treatment of essential boundary conditions and the determination of moving step size. On this basis, the essential boundary condition is applied by the displacement constraint equation method and the topology optimization is carried out by the adaptive moving step interpolation method. The main research contents are as follows: 1. This paper analyzes the influence of the treatment method of essential boundary conditions on the computational efficiency in the structural analysis of meshless Galerkin method, and puts forward the application of the displacement constraint equation method to the essential boundary conditions, and expounds the basic theory of the displacement constraint equation method. The results show that the displacement constraint equation method can improve the calculation efficiency and save the storage capacity on the premise of ensuring the accuracy of the calculation results. 2. The efficiency of Lagrange multiplier method and displacement constraint equation method in topology optimization is compared, and the superiority of displacement constraint equation method in improving topology optimization efficiency is further confirmed. In this paper, the causes of the degradation of the minimum density of moving particle method nodes are analyzed, and the adaptive moving step insertion method is proposed. Some examples are analyzed and discussed by Visual Fortran, and the advantages of this method in improving the efficiency of topology optimization are verified. 3. The influence of the decision value of mobile node density on the topology optimization results and optimization efficiency is analyzed and discussed. The relationship between the decision value of mobile node density and the number of iterations and the continuity of the final topological boundary is obtained, which provides a breakthrough for the improvement of the optimization algorithm. 4. The reasons for the number of iterations and the time consuming of adaptive step insertion method in calculating the minimum density of nodes less than 0.1 are analyzed. Combined with the influence of mobile node density decision value on the optimization iterative process, an improved optimization algorithm is proposed. The result of example analysis shows that the improved optimization algorithm shortens the number of iterations and computation time when the minimum density of nodes is less than 0.1, and improves the efficiency of topology optimization. In this paper, the essential boundary conditions are dealt with by using the displacement constraint equation method, and the topological optimization is carried out by using the adaptive moving step insertion method, which successfully eliminates the degradation of the minimum density and gradient values of nodes in the iterative process. The improved optimization algorithm based on the previous analysis shortens the computing time when the minimum density of the node is less than 0.1 and improves the efficiency of topology optimization while ensuring the quality of the results.
【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
本文编号：2340339
[Abstract]:As a new topology optimization method, moving particle method successfully eliminates some numerical instability in the optimization process. However, as with other topology optimization methods, the moving particle method also has the problems of long calculation time and low efficiency, which restricts its application in engineering practice. In this paper, the factors affecting the efficiency of topology optimization are studied from two aspects: the treatment of essential boundary conditions and the determination of moving step size. On this basis, the essential boundary condition is applied by the displacement constraint equation method and the topology optimization is carried out by the adaptive moving step interpolation method. The main research contents are as follows: 1. This paper analyzes the influence of the treatment method of essential boundary conditions on the computational efficiency in the structural analysis of meshless Galerkin method, and puts forward the application of the displacement constraint equation method to the essential boundary conditions, and expounds the basic theory of the displacement constraint equation method. The results show that the displacement constraint equation method can improve the calculation efficiency and save the storage capacity on the premise of ensuring the accuracy of the calculation results. 2. The efficiency of Lagrange multiplier method and displacement constraint equation method in topology optimization is compared, and the superiority of displacement constraint equation method in improving topology optimization efficiency is further confirmed. In this paper, the causes of the degradation of the minimum density of moving particle method nodes are analyzed, and the adaptive moving step insertion method is proposed. Some examples are analyzed and discussed by Visual Fortran, and the advantages of this method in improving the efficiency of topology optimization are verified. 3. The influence of the decision value of mobile node density on the topology optimization results and optimization efficiency is analyzed and discussed. The relationship between the decision value of mobile node density and the number of iterations and the continuity of the final topological boundary is obtained, which provides a breakthrough for the improvement of the optimization algorithm. 4. The reasons for the number of iterations and the time consuming of adaptive step insertion method in calculating the minimum density of nodes less than 0.1 are analyzed. Combined with the influence of mobile node density decision value on the optimization iterative process, an improved optimization algorithm is proposed. The result of example analysis shows that the improved optimization algorithm shortens the number of iterations and computation time when the minimum density of nodes is less than 0.1, and improves the efficiency of topology optimization. In this paper, the essential boundary conditions are dealt with by using the displacement constraint equation method, and the topological optimization is carried out by using the adaptive moving step insertion method, which successfully eliminates the degradation of the minimum density and gradient values of nodes in the iterative process. The improved optimization algorithm based on the previous analysis shortens the computing time when the minimum density of the node is less than 0.1 and improves the efficiency of topology optimization while ensuring the quality of the results.
【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
【参考文献】
相关硕士学位论文 前4条
1 陈敏;基于EFG法的连续体结构模态拓扑优化研究[D];湘潭大学;2010年
2 曾兴国;基于移动粒子法的连续体结构拓扑优化研究[D];湘潭大学;2011年
3 伍贤洪;基于自适应的EFG法连续体结构拓扑优化研究[D];湘潭大学;2011年
4 张建平;基于RKPM的结构动力分析及形状优化研究[D];湘潭大学;2007年
本文编号：2340339
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