基于拓展多尺度有限元的点阵材料结构最小柔顺性设计

本文应用拓展的多尺度有限元法（Extended Multiscale Finite Element Method)，以微观构件的截面积为设计变量，研究了体积约束下点阵材料构成结构的最小柔顺性设计问题。建立了适应具有复杂几何形状和载荷边界的点阵材料结构的优化模型，应用序列二次规划算法对悬臂梁和L形梁算例在线性边界条件和周期性边界条件下进行了优化设计，讨论了点阵材料微结构尺寸效应对优化结果的影响，验证了优化模型和求解算法的可靠性，为点阵材料应用于复杂实际工程结构的优化设计提供了新的技术手段。

MINIMUM COMPLIANCE DESIGN OF LATTICE MATERIALS BASED ON EXTENDED MULTISCALE FINITE ELEMENT METHOD

The paper deals with the problem of minimum compliance design of structures composed of periodic lattice materials with the sectional area of micro components as design variables under volume constraints with Extended Multiscale Finite Element Method. Considering unit cells with finite size, optimization model which adapts to the structure with complex geometry and loading conditions has been established. The size effect of micro-structure of the lattice materials is discussed. Cantilever and L-shaped beams under linear boundary condition and periodic boundary condition are optimized with sequential quadratic programming algorithm. The reliability of the optimization model and algorithm are verified by the numerical examples. The paper presents a new approach for optimization of lattice materials to compose engineering constructions.