基于扩展多尺度有限元法的含液闭孔材料拓扑优化

基于扩展多尺度有限元方法，提出了含液闭孔结构多尺度拓扑优化方法。该多尺度优化方法旨在研究含液闭孔胞元布局对整体含液闭孔结构力学性能的影响。首先针对含液闭孔结构的整体结构柔顺性问题，采用类似SIMP模型对结构的宏观粗网格等效刚度阵进行插值，建立含液闭孔结构柔顺性的拓扑优化列式；其次，针对含液闭孔材料能够利用胞体内部液体腔体积增量产生变形的特性，提出含液闭孔材料柔性机构的概念，并以结构指定位置方向输出位移为目标，建立液体体积膨胀作用下的含液闭孔柔性机构多尺度拓扑优化数学模型。本文基于自主软件平台SiPESC完成了程序研发，并通过数值算例验证了所提出的拓扑优化方法的有效性。

TOPOLOGY OPTIMIZATION OF CLOSED LIQUID CELL MATERIALS BASED ON EXTENDED MULTISCALE FINITE ELEMENT METHOD

A topology optimization method based on extended multiscale finite element method is developed to design the closed liquid cell materials. The main goal of the methodology is to discuss the optimal layout of the closed liquid cells, which can be considered as the basic element of the closed liquid cell structure. Firstly, the multiscale topology optimizations focus on finding the optimal distributions of closed liquid cells in terms of minimum compliance of the whole structure, in which the design domain is discretized by the multiscale coarse elements and a “SIMP-like” density-based approach is employed. Subsequently, due to the fact that the closed liquid cell materials can be used to design compliant mechanisms, the topology optimization problems of such kind of compliant mechanism are investigated based on the multiscale methods. Finally, software implementation is based on SiPESC and numerical examples are carried out to validate the accuracy of the multiscale topology optimization method for the closed liquid cell materials.