柔顺机构拓扑优化设计中的拓扑图提取理论和方法

Aiming to the problems existing in the topology extraction including intermediate elements, checkerboards and the contour extraction, a complete system of the theory and methodology of the topology extraction in the topology optimization design for compliant mechanisms is studied to establish in this project. Firstly, binary constraints on design variables are relaxed based on the scheme of solid isotropic material with penalization (SIMP). Invalid materials are deleted hierarchically by combining the volume constraint continuation and evolutionary scheme. Therefore, a method of the evolutionary 0-1 topology optimization based on SIMP and the volume constraint continuation is founded. Secondly, virtual universe attraction constraints are imposed in the optimization model and the multi-constrained optimality criterion is derived. As a result, a method of circumventing checkerboards based on virtual universe attraction constraints is established. Further, an area factor of the element material is enforced in SIMP. And the optimality criterion considering the area factor is formulated. Meanwhile, varying topology boundaries are captured by employing the level set method during the process of updating design variables. Thus, a method of simultaneous optimization of the topology and contour is gained. At last, virtual universe attraction constraints considering boundary elements are given. And the multi-constrained optimality criterion with the area factor is written. Also, the volume constraint continuation and evolutionary scheme considering boundary elements is presented. In this way, the complete system of the theory and methodology of the topology extraction for compliant mechanisms is achieved. Besides, by using the three-dimensional simulation and displacement experiment, the system of the theory and methodology of the topology extraction is revised and improved, which enables compliant mechanisms designed by using the topology optimization to be good for the engineering application directly.

针对拓扑图提取中的中间单元、棋盘格和轮廓提取问题，本项目研究建立完整的柔顺机构拓扑优化设计中的拓扑图提取理论和方法体系。首先基于SIMP松弛设计变量，结合体积约束延拓和渐进方案，分层去除无效材料，建立基于SIMP和体积约束延拓的渐进0-1拓扑优化方法；然后在优化模型中施加拟万有引力约束，推导多约束最佳准则，建立基于拟万有引力约束的消除棋盘格的方法；随后在SIMP中增加单元材料面积因子，确立考虑面积因子的最佳准则,在设计变量更新过程中利用水平集方法捕捉变化的拓扑图边界，建立基于SIMP和水平集方法的拓扑和轮廓同步优化方法。最后结合考虑边界单元的拟万有引力约束、考虑面积因子的多约束最佳准则和考虑边界单元的体积约束延拓和渐进方案，建立完整的柔顺机构拓扑图提取理论和方法体系。利用三维模拟仿真和位移实验，修正和完善拓扑图提取理论和方法体系，使基于拓扑优化方法所设计出的柔顺机构能够直接胜任于工程应用。

研究了一种黑白无铰链拓扑优化设计方法。首先寻找一个允许灰度边界的最佳拓扑，当得到一个适当的设计之后，将该解作为后续优化的起始点，以去除中间单元。建立了一个更新的最佳准则，引入一个阈值因子来逐渐抑制低密度单元。传统的最佳方法和所建议的新技术相继应用于设计过程。而且，为了克服去除中间单元过程中产生的一点铰链问题，建立了铰链去除策略。提出一种多层渐进黑白(0-1)拓扑优化设计方法。将拓扑图中无效的中间单元看成多余材料，在此基础上，采用体积比多层延拓方案，逐步逼近优化问题的目标体积比，同时，利用基于相对密度的单元渐进筛选方法，分层地去除设计域中的无效材料，保留其中的最有效材料，并逐层缩小拓扑优化模型的可利用材料域。提出一种基于无棋盘格约束的柔顺机构拓扑优化设计方法。首先分析拓扑优化结果中的棋盘格现象，然后建立消除棋盘格的约束条件，在此基础上建立具有消除棋盘格的设计变量更新最佳准则，推导无棋盘格约束灵敏度。提出一种基于梯度矢量流模型的柔顺机构拓扑图的轮廓提取方法。给出了不同的初始蛇模型及相应的模型演化方法，实现了柔顺机构拓扑图轮廓的自动提取。