几何约束条件下拓扑与形状统一优化方法研究

发布时间：2018-12-14 11:14

【摘要】：本课题受国家自然科学基金项目“几何约束条件下连续体结构拓扑与形状统一优化设计方法研究(50975107)”的支持。针对当前拓扑优化设计方法不能与形状优化、尺寸优化相融合的问题，本文提出了一种参数化水平集拓扑、形状、尺寸统一优化的方法，并将其推广到连续体结构的刚度设计，动力学优化设计中。首先，本文介绍了标准水平集法和参数化水平集法的基本理论，并分别比较了其优缺点。在此基础上，针对规则孔洞的尺寸或位置设计问题，将规则孔洞作为几何约束，，提出了一种参数化水平集尺寸优化设计方法，该方法同时包含了隐式表达和参数化表达的优点，为构建统一优化模型提供了前提条件。第二，将基于水平集法的拓扑形状优化模型与尺寸优化模型结合在一起，构建出统一优化模型，推导了灵敏度分析公式，并采用基于Kuhn-Tucker条件的优化准则法求解。同时，针对统一优化设计中出现的数值问题，如规则孔洞的多孔干涉问题，孔洞尺寸厚度问题，提出了采用尺寸约束和公差带的办法来解决。第三，提出了一种扩展有限元法来求解统一优化模型。拓扑优化的锯齿状边界问题一直没有得到很好的解决，本文采用扩展有限元法有效的解决了这一问题。该方法在边界单元处计算精度高，不仅提高了优化结果的边界光顺度，同时减少了计算时间，使得收敛过程更加稳定。最后，基于本文提出的水平集统一优化方法，同时考虑拓扑形状优化和尺寸优化，设计了一种新型的LED分拣臂，大幅度提高了分拣臂的一阶频率，该工程案例进一步验证了统一优化方法在动力学设计方面的适用性和精确性。
[Abstract]:This topic is supported by the project of National Natural Science Foundation of China, "study on the Unified Optimization Design method of Topology and shape of Continuum structures under geometric constraints (50975107)". Aiming at the problem that the current topology optimization method can not be combined with shape optimization and dimension optimization, a parameterized horizontal set topology, shape and dimension optimization method is proposed in this paper, which is extended to the stiffness design of continuum structure. Dynamic optimization design. Firstly, the basic theories of standard level set method and parameterized level set method are introduced, and their advantages and disadvantages are compared. On this basis, aiming at the problem of size or position design of regular holes, a parameterized horizontal set size optimization design method is proposed, which includes the advantages of implicit representation and parametric representation. It provides the precondition for constructing the unified optimization model. Secondly, combining the topological shape optimization model based on the level set method with the dimension optimization model, the unified optimization model is constructed, the sensitivity analysis formula is derived, and the optimization criterion method based on Kuhn-Tucker condition is used to solve the problem. At the same time, aiming at the numerical problems in the unified optimization design, such as the porous interference of regular holes and the hole size thickness, the method of dimension constraint and tolerance band is proposed to solve the problem. Thirdly, an extended finite element method is proposed to solve the unified optimization model. The sawtooth boundary problem of topology optimization has not been solved well, and the extended finite element method is used to solve this problem effectively. The method not only improves the boundary smoothness of the optimization results, but also reduces the calculation time and makes the convergence process more stable. Finally, based on the level set optimization method proposed in this paper, considering the topology optimization and size optimization, a new LED sorting arm is designed, which greatly improves the first order frequency of the sorting arm. The engineering case further verifies the applicability and accuracy of the unified optimization method in dynamic design.
【学位授予单位】：华中科技大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TH122

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