面向CAD系统的连续体结构形状与拓扑优化

针对当前连续体结构优化所面临的有限元模型与CAD模型转换困难，产品设计意图和结构工艺在优化过程中难以保持等问题，研究了面向CAD系统的连续体结构形状与拓扑优化方法。通过分析CAD几何表达和CAE网格划分特点，采用欧拉网格和扩展有限元法，建立面向结构优化的CAD/CAE模型融合机制；而后基于连续体物质导数，推导了CAD直接建模操作敏度，驱动CAD实体模型进行结构形状与拓扑优化。在此基础上，针对操作敏度量纲不一致问题，采用速度场均匀化方法，修正操作敏度，以提高优化收敛效率。通过三维CAD实体模型结构优化实例，验证了上述方法的可行性和求解效率。

Solution for Shape and Topology Optimization of Continuum Structures on CAD System

It is difficult to make conversion between the CAD model and the finite element model for the structural optimization, and to maintain the product design intent and structural manufacturing process during the optimization process. Therefore, a novel shape and topology optimization solution for continuum structure directly on CAD system is researched. Through analyzing the characteristic of CAD model and CAE mesh model, a scheme for integrating CAD/CAE model is developed with the employment of Euler mesh and extended finite element method. Based on the material derivative method, the structural sensitivities for direct modeling operations on the CAD systems are obtained to drive the CAD solid model to optimize the structural shape and topology. Furthermore, to alleviate the dimensional effect of different design parameters, a homogenization method is devised to modify the velocity field of various parameters so as to improve the convergence rate. Two examples of three dimensional solid CAD model are conducted to verify the proposed method. The experimental results show that the optimization method is validated and efficient on the CAD system.