【作者】 李栋；

【导师】 隋允康；

【作者基本信息】 北京工业大学 ， 固体力学， 2003， 硕士

【摘要】 本文根据隋允康教授提出的二级控制理论，将二维连续体结构的形状优化问题处理成序列二次规划问题进行了优化。本文工作的基本思路是：形状优化的研究者应当将主要精力放在模型化上，把优化理论与现有的通用性分析软件、结构优化模型建立方法结合起来，发展集分析与优化为一体的软件，用以满足工程的迫切需要。形状优化的难点主要有三点：一是设计变量与目标函数、约束的关系非常复杂，很难找到简单的显式关系，敏度求解困难；二是结构形状不易描述，形状变化不易控制；三是网格在优化过程中需要自动生成，而且会发生改变。二级控制是指在目标函数和设计变量之间加入两个中间变量——关键点和网格节点，建立设计变量控制关键点，关键点控制节点（网格）这两层控制关系，从而有效地解决了敏度的求解问题。通过设计单元和关键点，准确地描述和控制结构形状的变化。使用映射法在优化过程中对网格的生成和改变进行控制。因此，使用二级控制理论可以有效的解决二维连续体结构形状优化的主要困难。本文使用MSC.PCL语言在MSC.PATRAN&NASTRAN平台上实现了优化模块的二次开发，增加了二维连续体结构形状优化的功能。求解二次规划问题使用了Lemke法。本程序的优点在于结合了世界著名的结构分析软件的强大功能，成熟的前后处理界面，方便易用的建模手段和先进的优化理论。本文设计思路的可行性和程序的有效性通过若干算例得到证实。更多还原

【Abstract】 A program of shape optimization for two-dimensional continuum structures , which is carried out on MSC.PATRAN&NASTRAN panel, is described in this thesis, according to a two-phase control theory presented by Professor Sui yunkang , the optimization is treated as a Sequential Quadratic Programming problem.The research of shape optimization in this thesis focuses in the region of modelling of optimization, incorporating the advanced theory of optimization, general analysis software and the model of the various finite elements, with the purpose of meeting the urgent need of engineers.There are three difficulties in shape optimization: the first one is the relation between design variables and objective function, or between design variables and constrant function is not easy to find the simple apparent relation and the sensitivity. The second one both the structure shape describing and the shape changing control is difficult. The third one is that the mesh should be generated and changed automatically in the procession of optimizing.Two-phase control indicates that we can insert two mid-variables between objective function and design variables, which are the keypoints and nodes in the mesh. Thus we can form the two-layer control relation about control keypoint of design variables and control node(mesh) of keypoint, and solve the sensitivity problem effectively. By using the design unit and keypoint, a change of structural shape can be controlled and described precisely. Use the MSC.PATRAN to form the initial mesh, then control the mesh in the procession of optimizing using mapping method. Therefore, the difficulties can be solved by applying the Two-phase control method.The development of shape optimization module on MSC.PATRAN is implemented on the base of PCL language. Furthermore, the function of shape optimization for two-dimension continuum structures is augmented. The advantages of this program lie in incorporating the mighty function of the famous structure analysis software, mature handling interface of pre-process and post-process, convenient and usable finite element modelling theory and advanced optimizing theory.The idea of the research is verifed by some examples. And the reliability, the accuracy and the high-efficiency of the program have been testfied by the results of the exams.更多还原