Topology optimization with local stress constraints and continuously varying load direction and magnitude: towards practical applications
Topology optimization with local stress constraints and continuously varying load direction and magnitude: towards practical applications
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DOI：
10.1098/rspa.2022.0436
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发表时间：
2023-03
期刊：
影响因子：
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通讯作者：
Fernando V. Senhora;I. Menezes;Glaucio H. Paulino
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文献类型：
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作者：
Fernando V. Senhora;I. Menezes;Glaucio H. Paulino
拓扑优化问题通常考虑单一载荷工况或少量离散的载荷工况；然而，实际结构往往承受无数种载荷工况，这些工况在强度、位置和/或方向上可能有所不同（例如移动/旋转载荷或不确定的固定载荷）。这些载荷的变化性显著影响结构中的应力分布，在设计过程中应予以考虑。我们提出一种局部应力约束的拓扑优化公式，该公式考虑方向连续变化的载荷，以确保在更符合实际的载荷条件下结构的完整性。该问题通过增广拉格朗日方法求解，并且通过一系列解析表达式纳入载荷方向的连续范围，这些表达式能够计算所有可能载荷方向上的最坏情况最大应力。通过控制用于推导最坏情况载荷的载荷基向量的大小，也可以处理可变的载荷强度。几个二维和三维示例表明，拓扑优化设计对方向变化的载荷极为敏感。由该公式生成的设计更安全、更可靠，并且更适合实际应用，因为它们考虑了实际的载荷条件。
Topology optimization problems typically consider a single load case or a small, discrete number of load cases; however, practical structures are often subjected to infinitely many load cases that may vary in intensity, location and/or direction (e.g. moving/rotating loads or uncertain fixed loads). The variability of these loads significantly influences the stress distribution in a structure and should be considered during the design. We propose a locally stress-constrained topology optimization formulation that considers loads with continuously varying direction to ensure structural integrity under more realistic loading conditions. The problem is solved using an Augmented Lagrangian method, and the continuous range of load directions is incorporated through a series of analytic expressions that enables the computation of the worst-case maximum stress over all possible load directions. Variable load intensity is also handled by controlling the magnitude of load basis vectors used to derive the worst-case load. Several two- and three-dimensional examples demonstrate that topology-optimized designs are extremely sensitive to loads that vary in direction. The designs generated by this formulation are safer, more reliable, and more suitable for real applications, because they consider realistic loading conditions.