基于双向渐进结构优化法的“破损-安全”结构轻量化设计

Design of Lightweight and Fail-safe Structures Using Bi-directional Evolutionary Structural Optimization Method

“破损-安全”(fail-safe)设计通过冗余载荷路径设计提升结构的损伤容限(残余承载能力),是保障飞行器结构安全性的重要设计环节;然而,冗余结构形式不可避免地导致重量增加、效率降低,严重制约飞行器结构性能的进一步提升.论文基于双向渐进结构优化法(Bi-directional Evolutionary Structural Optimization),提出了一种“破损-安全”结构轻量化设计方法.具体地,设计方法采用“0/1”离散拓扑变量,以结构重量(材料用量)最小化作为优化目标,同时对局部破损结构的承载形变进行约束(低于安全阈值).针对渐进结构优化法难处理多设计约束的瓶颈,采用p范数法对局部破损结构的最大承载形变进行凝聚,并通过拉格朗日乘子将其耦合至优化目标函数,实现结构轻量化与“破损-安全”的同步设计.进一步地,并依据最大残余承载形变对局部区域破损之于“破损-安全”的影响程度进行判定,通过免除低影响局部破损区域的残余承载形变分析与约束,大幅度地提升了优化设计效率.通过系列基准测试算例,验证了论文“破损-安全”设计方法的有效性及高效性.

The fail-safe designed structures with redundant load paths exhibit a high tolerance to damage(residual load-bearing capacity),which is of essential significance to the safety of flight vehicles.However,the addition of redundant structures due to safety considerations inevitably increases the weight of flight vehicles and thus reduces flight efficiency.This study aims to use the bi-directional evolutionary structural optimization(BESO)method to design lightweight and fail-safe structures.Specifically,the design method with"0/1"discrete topology variables minimizes the structural weight(material volume)while constraining the residual load-bearing deformation of locally damaged structures to be less than a safety threshold.To break through the bottleneck of the BESO method in dealing with multiple constraints,the deformation constraints are aggregated by the p-norm global measure.The aggregated p-norm constraint is augmented into the design objective with the introduction of a Lagrange multiplier,achieving simultaneously the lightweight and the fail-safe designs.The effectiveness and efficiency of the proposed method is demonstrated through a series of benchmarks.Compared with the classical density-based methods,the proposed method realizes a lightweight fail-safe design with more robust structural branches,clearer load transfer paths,and a better load-bearing performance.However,considering all fail cases at each iteration step will cause excessive computational costs and hinder the engineering application of this method.Therefore,two efficiency-improvement schemes are proposed.(i)The optimization iterations can be reduced by introducing the initial design domain filled with holes.(ii)The significance of local region to the damage tolerance is calibrated according to the maximum residual load-bearing deformation.The design efficiency can be considerably improved by alleviating the residual load-bearing deformation analyses and constraints of low-significant local regions.Our study shows that different initial topologies and different residual deformation calibration thresholds lead to different optimization structures,and they both possess cross-supported forms and have similar fail-safe performances.With the efficiency-improvement schemes,the proposed method is suitable for the fail-safe designs under large-scale localized fail conditions,and can be straightforwardly applied to 3D lightweight fail-safe designs.It has a great potential for aerospace engineering applications.