骨骼重建拓扑优化方法的理论研究和数值模拟

发布时间：2018-01-17 00:18

本文关键词：骨骼重建拓扑优化方法的理论研究和数值模拟　出处：《北京工业大学》2009年硕士论文　论文类型：学位论文

【摘要】： 本文基于隋允康教授提出的ICM(Independent Continuous and Mapping,即独立、连续、映射)结构拓扑优化方法,建立了骨骼重建的拓扑优化模型,并运用对偶方法进行模型转换,用序列二次规划方法进行了求解,研究了连续体结构拓扑优化方法在骨骼重建方面的应用。并利用PCL语言对MSC.Patran进行二次开发,通过数值算例,将理论研究与数值模拟相结合,为实际应用提供了重要的理论依据。本文主要研究内容为: (1)研究了在应力作用下骨骼重建的拓扑优化。以骨骼结构的质量最小为目标,以应力为约束,利用应力全局化方法将局部应力约束转化为结构总应变能约束,建立了骨骼重建的拓扑优化模型,并运用对偶规划理论对模型进行了求解。 (2)采用ICM优化方法对不同骨骼结构的模型进行了数值模拟。对于相同的骨骼模型,分别对结构在不同应力、不同网格、不同载荷、不同材料参数及优化模型中取不同过滤函数的情况进行了研究。数值模拟的结果与实际骨骼结构类似,证明了该方法的可行性。 (3)根据上述优化模型和解法,利用PCL语言对MSC.Patran软件进行了二次开发,对在应力约束下的二维、三维骨骼重建拓扑优化问题生成了优化模块,为骨骼重建拓扑优化理论从概念设计走向实际应用提供了一条新途径。
[Abstract]:This paper is based on the topology optimization method of ICM(Independent Continuous and mapping proposed by Professor Sui Yunkang. The topology optimization model of bone reconstruction is established, and the dual method is used to transform the model, and the sequential quadratic programming method is used to solve the problem. The application of topology optimization method of continuum structure in bone reconstruction is studied, and the secondary development of MSC.Patran is carried out by using PCL language, and a numerical example is given. The combination of theoretical research and numerical simulation provides an important theoretical basis for practical application. The main contents of this paper are as follows: 1) the topological optimization of bone reconstruction under stress is studied. The minimum mass of bone structure is the objective and the stress is the constraint. The local stress constraint is transformed into the total strain energy constraint by using the stress globalization method, and the topological optimization model of bone reconstruction is established, and the model is solved by dual programming theory. (2) the ICM optimization method is used to simulate the different bone structure models. For the same bone model, the different stresses, different grids and different loads are applied to the same bone model. Different material parameters and different filtering functions in the optimization model are studied. The results of numerical simulation are similar to the actual skeleton structure, which proves the feasibility of this method. 3) according to the above optimization model and solution, the MSC.Patran software is redeveloped by using PCL language, and the two dimensions under the stress constraint are analyzed. The topology optimization problem of three-dimensional bone reconstruction generates an optimization module, which provides a new way for the theory of topology optimization of bone reconstruction from conceptual design to practical application.
【学位授予单位】：北京工业大学
【学位级别】：硕士
【学位授予年份】：2009
【分类号】：R346

【参考文献】