基于光滑变形隐式曲线/曲面的结构拓扑优化方法研究

Continuum structural topology optimization has become an important technology for the creative design of high performance structural configurations. Keeping up with the research hotspots and development trend, this project aims to form an engineering-oriented topology optimization method characterized by high efficiency and high precision, which will be carried out in the following three stages: firstly, the topology optimization method of 2D structures via smoothly deformable implicit curves will be improved; secondly, the topology optimization method of 3D structures via smoothly deformable implicit surfaces will be developed; thirdly, the advantages of the proposed method will be exploited to solve the problems related to the topology optimization design of high performance structures. .The details are as follows: (1) the initial layout dependency problem will be eliminated by means of topological derivative theory and perimeter constraint method, and the advanced measures related to the effective use and tapping the potential of the two technologies will be explored; (2) the construction method of the smoothly deformable implicit surface characterized by very few parameters and high deformation capacity will be proposed, the key techniques for reducing the amount of recalculation and significantly improving calculation efficiency will be studied; (3) local stress constraints and engineering features will be considered in topology optimization design, and innovative solutions will be designed to solve the problems related to the excessive number of constraints, the overcomplicated engineering features as well as the singularity phenomenon. The more complicated and more challenging problems concerning the design of high performance structural configurations will be solved thoroughly by enhancing the advanced topology optimization technology. Accordingly, the successful implementation of this project is of great significance in theory and practical value in engineering.

连续体结构拓扑优化已发展成为高性能结构创新构型设计的重要技术手段。本项目紧跟当前拓扑优化方法的研究热点和发展趋势，拟在完善现有基于光滑变形隐式曲线的二维结构拓扑优化方法的基础上，发展出基于光滑变形隐式曲面的三维结构拓扑优化方法，进而发挥所提方法优势以解决高性能结构拓扑优化设计难题，最终形成面向工程设计需求的高效率高精度拓扑优化方法。.研究内容包括：(1)利用拓扑导数理论和周长约束方法消除初始布局依赖性，探究有效应用这两项技术并能挖掘其潜力的先进措施；(2)提出参数极少且变形能力强的光滑变形隐式曲面的构建方法，研究减少重复计算并充分提高固定网格分析效率的关键技术；(3)施加局部应力约束和工程特征约束，针对约束数量过多、工程特征复杂以及奇异解问题等设计出创新性解决方案。本项目的成功实施能够推动先进拓扑优化技术深入解决更复杂、更具挑战性的高性能结构构型设计问题，具有重要的理论意义和工程应用价值。

连续体结构拓扑优化已发展成为高性能结构创新构型设计的重要技术手段。然而，当前主流拓扑优化方法普遍存在着变量数目庞大、力学响应分析精度低和/或材料边界模糊非光滑等问题，严重制约了该技术工程应用的深度和广度。.本项目通过引入高精度固定网格分析技术，致力于实现面向工程设计需求的高效率高精度拓扑优化设计。在结构设计过程中使用本项目研发出的方法和技术，不仅可以尽可能地挖掘材料潜力以得到具有清晰光滑边界的优化设计结果，还能高精度地满足材料许用强度约束和复杂工程特征约束需求。主要研究内容与重要结果如下：.形成一种固定网格下高效率高精度拓扑优化设计方法——自适应泡泡法。为继承传统拓扑优化泡泡法变量少、精度高等优点，并克服其网格重划频繁、孔洞合并操作繁琐等不足，本工作首先采用有限胞元固定网格分析方法计算结构力学响应，在优化过程中无需网格更新和重划分，就能保证较高的分析精度；进而根据拓扑导数信息指导结构区域中孔洞的引入，不仅消除了优化结果对孔洞初始布局的依赖性，还能有效控制设计变量的数量；然后引入拓扑导数阈值和孔洞影响区域新概念，实现了孔洞引入频次和位置的自适应调节，保证了拓扑优化过程的数值计算稳定性；最后采用光滑变形隐式曲线描述孔洞边界，不仅设计参数少、变形能力强，而且便于处理孔洞间的融合/分离操作以及与固定网格分析方法的有机结合。.数值算例表明，本工作提出的自适应泡泡法扑优化设计方法能够消除传统泡泡法因采用拉格朗日网格和参数化B样条曲线模型而存在的实施困难，在固定网格下采用很少的设计变量就可获得边界光滑清晰的优化结果，并且无需后处理就可以直接导入到商用CAD和CAE软件中，有利于进一步的分析校核和加工制造。近期的工作已实现了基于自适应泡泡法的三维结构拓扑优化设计，并施加了局部应力约束，还将工程特征引入到了设计区域中，有力推动着自适应泡泡法深入解决更复杂、更具挑战性的高性能结构构型设计问题。