双向渐进结构拓扑优化方法的改进及应用

发布时间：2018-01-05 10:18

本文关键词：双向渐进结构拓扑优化方法的改进及应用　出处：《哈尔滨工程大学》2012年硕士论文　论文类型：学位论文

【摘要】：随着拓扑优化在结构设计在初始阶段中体现出来的创新性受到越来越多的认可，，结构拓扑优化成为了结构优化设计领域的热点研究对象。与尺寸优化和形状优化等优化方法相比，结构拓扑优化在结构设计之初就能给设计者一个不需要任何工程经验的概念设计，对工程设计人员更具吸引力。进行连续体结构的拓扑优化数学模型建立有多种方式，涉及的变量较多，同时又各具优缺点，使得拓扑优化的工程应用未能普及。本文研究的双向渐进结构优化方法（简称BESO方法）具有算法简单、与有限元分析程序连接容易等优点，在结构拓扑优化中的应用越来越广。本文以连续体结构为研究对象，对双向渐进结构拓扑优化方法与应用进行讨论，通过对其进行改进以提高其合理性、通用性以及工程实际应用能力。本文首先针对现阶段的渐进结构拓扑优化方法，总结归纳其在应用中遇到的各类常见问题及解决方法，通过分析这些方法的优缺点，提出了基于遗传算法思想并结合网格过滤技术的改进方法，避免了拓扑优化常见的“棋盘格”、网格依赖性及进入局部最优解现象。从提高材料利用率的角度出发，分别建立了以柔顺性为目标函数的结构强度拓扑优化及基于模态灵敏度排序的模态频率最大化结构拓扑优化数学模型。通过Matlab编程实现了BESO方法的改进，以经典悬臂梁及“Michell”结构验证了本文提出改进方法的改进效果，同时对比目前通用的变密度拓扑优化方法验证了本文方法的优点。其次，因为工程实际中往往需要考虑强度，刚度，稳定性，模态等多种要求，本文对同时考虑应力和位移约束、模态和位移的多约束优化问题进行了研究。采用拉格朗日乘子法，分别以结构柔顺性均匀及模态频率最大化为目标函数，建立相应的多约束单元灵敏度值计算数学模型。第三，以高性能的有限元分析软件HyperWorks为平台，结合TCL与C语言进行软件二次开发。通过模块化编程操作将改进后的BESO方法在HyperWorks中实现，包括求解模型的前处理、BESO方法求解迭代曲线的同步显示、曲线编辑、结果后处理等，提高了该方法的通用性。最后针对结构粘附阻尼减振技术，结合BESO方法，提出一种适用于船舶中的大量板结构粘附阻尼材料减振时确定阻尼材料粘贴位置的方法。通过在一块两端约束的简单板结构中应用该方法验证了该方法的正确性，可以在工程实践中推广该方法。
[Abstract]:With the topology optimization in the initial stage of structural design reflected in the innovation is more and more recognized. Structural topology optimization has become a hot research object in the field of structural optimization design, compared with the optimization methods such as dimension optimization and shape optimization. Structural topology optimization can give designers a concept design without any engineering experience at the beginning of structural design. It is more attractive to engineers and designers. There are many ways to establish the mathematical model of topology optimization of continuum structure, which involve many variables, and at the same time, each has its own advantages and disadvantages. The bi-directional asymptotic structural optimization (BESO) method studied in this paper has the advantages of simple algorithm and easy connection with finite element analysis program. In this paper, taking continuum structure as the research object, the method and application of bi-directional asymptotic structural topology optimization are discussed, and the rationality of the method is improved by improving it. Generality and engineering practical application ability. In this paper, aiming at the current evolutionary topology optimization methods, we summarize the common problems and solutions encountered in its application, and analyze the advantages and disadvantages of these methods. An improved method based on genetic algorithm and mesh filtering technology is proposed to avoid the "checkerboard" commonly used in topology optimization. The phenomenon of grid dependence and local optimal solution is obtained from the point of view of improving the material utilization ratio. The mathematical models of structural strength topology optimization based on flexibility as objective function and modal frequency maximization structural topology optimization model based on modal sensitivity ranking are established respectively. The BESO square is realized by Matlab programming. The improvement of law. The improved method is verified by classical cantilever beam and "Michell" structure, and the advantages of this method are verified by comparing with the current general variable density topology optimization method. Secondly, because the strength, stiffness, stability, mode and other requirements are often considered in engineering practice, the stress and displacement constraints are considered in this paper. The multi-constraint optimization problem of modes and displacements is studied. The Lagrange multiplier method is adopted, and the objective functions are the uniformity of structural compliance and the maximization of modal frequency, respectively. A mathematical model for calculating the sensitivity value of multi-constrained elements is established. Third, take the high performance finite element analysis software HyperWorks as the platform. Combined with TCL and C language, the software is redeveloped. The improved BESO method is implemented in HyperWorks by modular programming operation, including the pre-processing of solving the model. The BESO method is used to solve the synchronous display of iterative curves, curve editing and post-processing of the results, which improves the generality of the method. Finally, the BESO method is used to reduce the vibration of the structure with adhesive damping. This paper presents a method for determining the position of damping material when a large number of plate structures in ships are attached to damping materials to reduce vibration. The correctness of the method is verified by applying this method to a simple plate structure with two ends of constraints. . This method can be popularized in engineering practice.
【学位授予单位】：哈尔滨工程大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TH122

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