基于双向渐进结构优化法的“破损-安全”结构轻量化设计

“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.

Design of lightweight and fail-safe structures using bi-directional evolutionary structural optimization method

Fail-safe designed structures with redundant load paths exhibit high tolerance to damage (residual load-bearing capacity), which is of essential significance to the safety of flight vehicles. Meanwhile, the redundant structural configuration resulted from safety consideration inevitably increases the weight and reduces consequently the efficiency of flight vehicle structures. This paper proposes to design lightweight and fail-safe structures using Bi-directional Evolutionary Structural Optimization (BESO) method. Specifically, the design method with "0/1" discrete topology variables minimizes structural weight (material volume), meanwhile constrains the residual load-bearing deformation of locally damaged structures below a safety threshold. To address 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 to the design objective with the introduction of a Lagrange multiplier, achieving simultaneous design for lightweight and fail-safe. Furthermore, the significance of local region to the damage tolerance is calibrated according to the maximum residual load-bearing deformation. The design efficiency can be largely improved by saving the residual load-bearing deformation analyses and constraints of the low-significant local regions. The effectiveness and efficiency of the proposed method is demonstrated through a series of benchmark design examples.