【作者】 雷平；

【导师】 高行山；

【作者基本信息】 西北工业大学 ， 工程力学， 2007， 硕士

【摘要】 连续体结构的拓扑优化设计是继结构形状优化设计和尺寸优化设计以后，在结构优化领域出现的一种全新的研究方向。结构拓扑优化设计属于概念设计，即在进行形状优化和尺寸优化前，寻求结构的最优拓扑形式，这样可以避免了设计过程中的盲目性。这在产品初始设计阶段具有重要意义。 论文研究了连续体结构的拓扑化模型及其材料插值方法、以及连续体结构拓扑优化问题的数值求解算法；讨论了拓扑优化中数值不稳定现象，指出了一些解决办法；研究了飞机座舱内的声环境，在连续体结构拓扑优化理论的基础上，将拓扑优化技术应用于飞机座舱内的减振降噪方面，取得了较好的效果。论文的主要研究工作： 1．研究了连续体结构的拓扑优化模型的描述方式及其材料插值模型，主要讨论了均匀化法和密度法(SIMP)插值模型；研究了拓扑优化求解算法，主要是优化准则算法(OC)和数学规划算法(MP)，推导了基于SIMP模型的优化准则算法和移动渐进线算法。 2．对优化结构中出现的棋盘格和网格依赖等数值不稳定现象进行了剖析和讨论。介绍了一些常见解决方法，并指出了一条解决思路，即利用SIMP模型，通过控制惩罚因子，对中间密度材料和棋盘格式进行惩罚，再采用敏度过滤技术，控制网格依赖问题。 3．研究了飞机座舱内的声环境，基于上述对连续体结构拓扑优化理论的研究，将拓扑优化方法引入到飞机座舱内的噪声控制中，通过算例验证了采用该方法进行减振降噪的可行性。更多还原

【Abstract】 The topology optimization design for continuum structure is a brand-new research direction which appears in the field of structure optimization design following structure shape optimization and size optimization design. The structure topology optimization design is a kind of conceptual design, and it is of the purpose that seeking the optimal topology decision for structure before shape and size optimization, which could avoid non-intention in the design procedure. This method is of vital significance at the beginning of the product design.The topology model of the continuum structure, material interpolation method and numerical solution method for the continuum structure topology optimization are introduced and described in this paper. The numerical instability phenomenon during topology optimization is also discussed and some possible solutions are presented. Based on fundamental research for continuum structure topology optimization, topology optimization technology is adopted to reduce noise in an aircraft cabin and good effect is obtained. The main research work in this paper is as follow:1. Topology depicting method and material interpolation schemes are studied. The homogenization method and SIMP method with material interpolation schemes are also summarized, Two optimization solution—optimization criteria (OC) method and mathematic programming (MP) method are stated. The OC algorithm and the MMA (method of moving asymptotes) algorithm based on SIMP approach are deduced and used for the topology optimization problem of continuum structure.2. Numerical instabilities during topology optimization, such as checkerboard and mesh dependency, are analyzed and investigated. A solution which uses SIMP model to adjust penalty factor to control checkerboard and adopts filtering the sensitivities technology to control mesh dependency, is pointed out to avoid numerical instability phenomenon.3. The acoustics environment in aircraft cabin has been research. Based on theory research for continuum structure topology optimization, the structural topology optimization method is introduced to reduce noise in aircraft cabin. The computational results show the efficiency of topology optimization method in noise reduction.更多还原