渐进结构优化方法及其在回转体拓扑优化中的应用研究

发布时间：2018-06-07 14:16

本文选题：渐进结构优化 + 拓扑优化　；参考：《重庆大学》2012年硕士论文

【摘要】：科学技术的不断发展对结构的力学性能和经济性提出了越来越高的要求，，从而促进设计方法的研究和迅速发展。结构最优化设计正是这样一个迅速发展的设计领域。结构优化方法使得设计人员可进行主动、创造性的设计，而结构拓扑优化则是后续的形状、尺寸优化设计的基础。飞轮等回转体作为一类重要的机械零件结构类型，其拓扑形式不仅影响着这类物体力学性能，同时影响如飞轮转动惯量等工作性能。本文采用渐进结构优化方法（ESO）对含有刚度、转动惯量、体积要求等信息的回转体进行拓扑优化研究。本文推导了离心力作用下的单元刚度灵敏度计算公式，并采用“硬杀”策略的双向渐进结构优化方法（BESO）对二维和三维的回转体进行优化分析。依据多目标优化的乘除法策略，提出了基于灵敏度乘除法的双向渐进结构优化的多目标处理方法，成功实现了某汽车驱动盘和某飞轮的多目标拓扑优化设计。同时对该方法在特殊情形下的失效做了分析。针对刚度灵敏度和转动惯量灵敏度不同的分布规律，提出了灵敏度再处理技术，以此平衡两种不同类型灵敏度对单元删增的影响，并指出灵敏度再处理技术是一种特殊的过滤技术。本文就回转体一定转动惯量下单元数目不可控的问题，提出了以最大刚度为优化目标，以转动惯量为约束下的渐进结构优化方法。结构的渐进变化仍依据体积的进化率，在转动惯量满足约束条件时，应尽量增大结构体积以最大程度提高结构刚度。进而实现了以最大刚度为优化目标，体积和转动惯量同时约束的多约束优化问题。在结构渐进到体积约束限且转动惯量不满足约束条件时，通过构造拉格朗日函数将单元转动惯量信息包含在单元灵敏度中，从而使转动惯量逐步向约束范围内逼近。依据提出的优化算法，实现了某飞轮的结构拓扑优化，算例表明此方法的正确性和有效性。
[Abstract]:With the development of science and technology, the mechanical properties and economy of structures are required more and more, thus promoting the research and rapid development of design methods. Structural optimization design is such a rapidly developing field of design. The structural optimization method enables designers to design actively and creatively, while structural topology optimization is the basis of subsequent shape and size optimization design. As an important structural type of mechanical parts, the topological form of flywheel iso-rotary body not only affects the mechanical properties of this kind of object, but also affects the working performance such as the moment of inertia of flywheel. In this paper, an evolutionary structural optimization method (ESO) is used to study the topology optimization of a rotary body with information such as stiffness, moment of inertia and volume requirement. In this paper, the formulas for calculating the sensitivity of element stiffness under centrifugal force are derived, and the bi-directional progressive structural optimization method of "hard kill" strategy is used to optimize the two-dimensional and three-dimensional rotary bodies. According to the strategy of multiplication and division of multi-objective optimization, a multi-objective method of bidirectional progressive structural optimization based on sensitivity multiplication and division method is proposed, and the multi-objective topology optimization design of a driving disk and a flywheel is successfully realized. At the same time, the failure of the method in special cases is analyzed. Aiming at the different distribution of stiffness sensitivity and moment of inertia sensitivity, a sensitivity reprocessing technique is proposed to balance the effects of two different types of sensitivity on element deletion. It is pointed out that sensitivity reprocessing is a special filtering technique. In this paper, for the problem that the number of elements is not controllable under a certain moment of inertia of a rotary body, a progressive structural optimization method with the maximum stiffness as the optimization objective and the moment of inertia as the constraint is proposed. The gradual change of the structure is still based on the evolution rate of the volume. When the moment of inertia satisfies the constraint condition, the volume of the structure should be increased as much as possible in order to increase the stiffness of the structure to the maximum extent. Furthermore, the multi-constraint optimization problem with the maximum stiffness as the optimization objective and the volume and moment of inertia simultaneously constrained is realized. When the structure is progressive to the volume constraint limit and the moment of inertia does not satisfy the constraint conditions, the information of the element moment of inertia is included in the element sensitivity by constructing the Lagrangian function, which makes the moment of inertia gradually approximate to the constraint range. According to the proposed optimization algorithm, the structure topology optimization of a flywheel is realized. The example shows that the method is correct and effective.
【学位授予单位】：重庆大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TH133.7

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