基于等几何分析的板壳结构形状拓扑协同优化

Simultaneous Shape-Topology Optimization of Shell Structures Based on Isogeometric Analysis

板壳结构轻量化设计是工程中的常见问题,采用有限元法对板壳结构进行拓扑优化时,难以获得高质量的网格以精准描述几何模型,且单独使用拓扑优化受制于初始设计空间。提出了一种基于等几何分析的形状拓扑协同优化方法,该方法执行先形状优化、后拓扑优化的步骤,在最佳结构形状的基础上实现最佳材料布局的优化目标。相比于其他组合形式的优化机制,极大地提高了计算精度与计算效率。采用3个数值算例验证了本方法的有效性与高效性,结果表明,与经典等几何拓扑优化方法相比,可得到更高性能的优化结构,有助于进一步拓宽结构优化的应用范围。

The lightweight design of shell structures is a common problem in engineering,using the finite element method to optimize the topology of shell and plate structures is difficult to achieve high-quality mesh to accurately describe the geometric model,and using the topology optimization alone will limit the design space.A simultaneous shape-topology optimization method based on isogeometric analysis is proposed in this paper.The method performs the steps of shape optimization first and topology optimization later,and realizes the optimization goal of the best material layout on the basis of the best structure shape.Compared with other combined forms of optimization mechanisms,the computational accuracy and computational efficiency are greatly improved.Three numerical examples were used to verify the effectiveness and efficiency of the method.The results show that the present method achieves a higher performance optimized structure compared with the classical isogeometric topology optimization method.This will help to further broaden the scope of applications for structural optimization.