Topology optimization method of continuum structure considering fail-safe design under stress constraints

应力约束下考虑破损-安全设计的连续体结构拓扑优化方法

¹ Yangjiang Nuclear Power Co., Ltd., Yangjiang 529941, China
² Suzhou Nuclear Power Research Institute Co., Ltd., Suzhou 215004, China
³ School of Mechanics and Transportation Engineering, Northwestern Polytechnical University, Xi'an 710072, China

Received: 29 August 2024

Abstract

In engineering structures, local damage can reduce significantly overall performance, attracting widespread attention. However, the existing topology optimization methods often overlook the impact of local damage on structural safety, limiting their effectiveness in addressing this challenge. To this end, a topology optimization method of continuum structures in terms of the fail-safe design principles is proposed, where the fixed-shape damage regions are designated as the local damage patterns. The optimal model is established with the objective of minimizing structural volume under stress constraints. An optimization algorithm is developed based on the independent continuous mapping (ICM) method, with sensitivity analysis conducted by using the adjoint method and optimization problem-solving carried out by using the dual programming theory. Using classic L-shaped beams as case, the effects of the distributions and shapes of local damage on the optimal configurations is investigated. Numerical results show that optimal configurations incorporating fail-safe design principles are more complex and contain greater redundancy, therefore reducing the sensitivity to local damage. Furthermore, the damage distributions and shapes yield varying topological configurations. The present method effectively identifies the most unfavorable damage distribution locations within structures, providing the valuable guidance for designing the safety performance of engineering structures.

摘要

在工程结构中, 局部破损可能显著降低其整体性能, 这一问题引起了广泛关注。然而, 现有的拓扑优化方法往往忽略了局部破损对结构安全性的影响, 难以有效应对这一挑战。为此, 提出了一种基于破损-安全设计的连续体结构拓扑优化方法, 指定固定形状的损伤区域作为局部破损模式, 并以最小化结构体积为目标、以应力为约束建立优化模型。基于独立连续映射法(ICM)建立优化算法, 采用伴随法进行灵敏度分析, 利用对偶规划理论求解优化模型。以悬臂梁等经典结构作为研究对象, 探讨了不同的局部破损分布情况和形状对优化构型的影响规律, 数值算例结果表明: 考虑破损-安全设计原则的优化构型更加复杂, 同时具有更多冗余, 从而降低了对局部破损的敏感性; 局部破损区域的不同分布情况和形状会产生不同的拓扑优化构型; 所提方法可识别结构中最不利的破损分布位置, 为工程结构的安全性能设计提供了有力参考。