基于拓扑优化的点阵-加筋板式结构设计方法

A method of designing plate structure consisting of lattices and stiffeners based on topology optimization

针对高超声速飞行器仪器舱设备安装板结构轻量化和提高静/动力学性能的设计需求,融合轻质点阵结构与传统加筋结构的优点,提出一种点阵-加筋板式结构方案并建立了拓扑优化设计方法。利用均匀化等效方法计算点阵结构的宏观等效力学性能,将其作为一种虚拟材料,建立实体材料-虚拟材料插值模型。以结构整体质量为约束,整体柔顺度最小为目标建立拓扑优化问题,实现点阵-加筋板式结构布局优化设计。以飞行器设备安装板为例,分别完成了传统加筋结构和点阵-加筋板式结构优化设计。力学性能分析表明,在相同质量条件下,点阵-加筋板式结构方案具有更好的力学性能,大过载下的最大变形降低11.17%,简谐激励下位移响应峰值降低73.81%。

In order to satisfy the lightweight design requirements of the equipment mounting plate in the hypersonic vehicle instrument cabin and improve its static/dynamic performance,a novel structure consisting of both lattices and stiffeners are studied and topology optimization method is proposed in this paper.This structure combines the advantages of lattice structures and conventional stiffened structures.First,the lattice structure is regarded as a kind of virtual material,and its equivalent mechanical properties are calculated by the homogenization method.Then,a marerial interpolation model of the virtual and solid materials are established.A topology optimization problem to minimize the mean compliance under the mass constraint is proposed to realize the layout optimization design of stiffened structure with lattices.Taking an equipment mounting plate as an example,the optimization design of the traditional stiffened structure and the novel stiffened structure with lattices is completed,respectively.Numerical analysis indicates that the lattice stiffened plate structure provides advantageous mechanical performation in the condition of the same weight.The maximum deformation under inertial force is reduced by 11.17%and the peak displacement response under harmonic excitation is reduced by 73.81%by using the stiffened structure with lattices.