连续纤维增强复合材料结构多尺度拓扑优化设计

Multi-scale topology optimization for continuous fiber-reinforced composite structures

连续纤维增强复合材料具有重量轻、比强度和比模量高的特点,日益受到航空航天等高端装备制造领域的青睐,同时连续纤维3D打印技术的发展使具有复杂几何构型和纤维分布的复合材料结构制造成为可能。为发挥复合材料多尺度的可设计性及获得更好的结构性能,本文基于独立连续拓扑变量提出了一种连续纤维复合材料结构多尺度拓扑优化方法。该方法引入基于主应力的纤维方向插值策略,解决纤维取向优化过程中易陷入局部最优的问题,实现连续纤维复合材料结构宏观拓扑、微观纤维方向和纤维疏密的并行优化设计。采用移动渐近算法(MMA)进行优化求解,数值算例证明了提出方法的有效性和稳定性,对连续纤维复合材料结构设计和路径规划具有指导意义。

Continuous fiber-reinforced composites are increasingly favored in high-end equipment manufacturing fields such as aerospace engineering due to their lightweight,high specific strength,and high specific modulus.Meanwhile,the development of continuous fiber 3D printing technology makes it possible to fabricate structures with complex geometric configurations and fiber distribution.To sufficiently utilize the multi-scale designability of composites and obtain better structural properties,a multi-scale topology optimization method for continuous fiber-reinforced composite structures based on independent continuous topology variables is proposed in this paper.This method introduces a fiber orientation interpolation strategy based on principal stresses to determine local optima in the fiber angle optimization process,and realizes the concurrent optimization design of macro-topology,micro-fiber orientation and density of continuous fiber composite structures.Topology and fiber orientation design variables are updated through the method of moving asymptotes(MMA).Numerical examples are provided to verify the effectiveness and stability of the proposed method,which has guiding significance for the structural design and path planning of continuous fiber-reinforced composite structures.