快速优化薄板中各向异性材料分布的等效变形模量算法

An equivalent⁃deformation⁃modulus algorithm for fast optimization of anisotropic material distribution in thin plates

各向异性材料广泛存在于各种机械设备的承重构件中。与各向同性材料不同,各向异性材料中不同材料相的分布和方向,可以根据载荷条件调整承重构件的力学性能。本文提出了一种各向异性材料分布的优化方法,即等效变形模量(EDM)算法,以有效地优化各向异性薄板的承载能力。该算法实现了对薄板抗弯能力的多模态协同优化,解决了传统优化算法中特征值重叠的问题,在航空领域中将起到重要作用。以短纤维增强聚合物薄板的纤维取向优化为例,在不改变薄板质量和形状的前提下,与传统优化算法相比,EDM算法可以将临界屈曲载荷提高28.9%,将计算成本降低98.1%。此外,EDM算法还被应用于机身中形状不规则的承重构件设计中,并使其临界屈曲载荷提高27.2%~30.8%。

Anisotropic materials widely exist in load-bearing components for various mechanical devices.Unlike isotropic materials,the distribution and orientation of different material phases in anisotropic materials can sensitively mediate the mechanical output of these components according to the loading conditions.In this paper,an optimization method for anisotropic material distribution,named Equivalent-Deformation-Modulus(EDM)algorithm,is proposed to efficiently optimize the load-bearing ability of anisotropic thin plates.This EDM algorithm will play an important role in the aviation,for it enables the multi-modal co-optimization for the buckling resistance of thin plates,and solves the problem of overlapping eigenvalue in traditional optimization algorithm.Taking the optimization of fiber orientation in short fiber reinforced polymer thin plate as an example,without changing the mass and shape of the plate,this EDM algorithm can improve the critical buckling load by 28.9%and reduce the computational cost by 98.1%,compared to traditional optimization algorithm.The EDM method was also applied to designing a load-bearing component in the airframe with an irregular shape by increasing the critical buckling load by 27.2%-30.8%.