基于Ordered SIMP插值模型的 点阵-实体复合结构拓扑优化设计方法

为了提高点阵材料结构件的力学性能,提出了一种基于Ordered SIMP方法的点阵-实体复合结构拓扑优化方法.采用一种三维X型微结构单元作为点阵材料,通过数值拟合建立点阵材料相对密度与其等效物理属性之间的函数关系.在宏观结构拓扑优化问题中,以点阵材料等效密度为设计变量,基于Ordered SIMP插值方法建立点阵材料和实体材料相结合的多材料插值模型,进而,以材料体积用量为约束,以结构柔度最小化为目标实现点阵-实体复合结构的多尺度拓扑优化设计.通过数值算例和实验测试表明,相比于仅使用点阵材料填充的设计,本方法能够获得更好的结构刚度.

Topology Optimization Method for Lattice-Solid Structure Design Based on Ordered SIMP Interpolation

To enhance the mechanical performance of lattice-infilled structures, this paper presents a multiscale topology optimization method based on ordered solid isotropic material with penalization (Ordered SIMP) interpola? tion model for lattice-solid hybrid structure design. The X-shape cubic cell is selected as the basic lattice structure, and polynomial functions are established through numerical fitting to relate the lattice relative density to its physical properties. Then, for macro structure topology optimization, relative densities of the macro elements are employed as the design variables, and a multi-material interpolation model spanning from variable-density lattices to solid is de? veloped based on the Ordered SIMP interpolation. Finally, a multiscale topology optimization problem is formulated to minimize the structural compliance of the lattice-solid hybrid structures subject to a material volume fraction constraint. Numerical examples and mechanical testing are presented to demonstrate the effectiveness of the proposed ap? proach compared with pure lattice-infilled structure designs.