论文标题
在不确定性下计算最坏情况限制负载的强大极限分析理论
Robust limit analysis theory for computing worst-case limit loads under uncertainties
论文作者
论文摘要
这项工作提出了一个新颖的理论框架，即可靠极限分析，即使用极限分析和强大的优化理论在不确定性存在下结构的极限载荷的计算。在材料强度不确定的情况下，我们首先得出了通用的稳健极限分析公式。我们讨论了对不确定强度特性建模的各种方法，并介绍了强大的强度标准的概念。我们为相应的不确定极限分析问题制定了静态和可调的鲁棒对应物。根据所选的强度不确定性模型，我们还讨论了可使用圆锥编程求解器数值实施的可拖动重新构造或近似值。在这些结果的基础上，我们还会在存在不确定性的情况下得出强大的极限分析公式。最后，各种应用说明了提出的框架的多功能性，包括具有不确定的内聚力和摩擦角的强大MOHR-COULOMB标准，结构的限制载荷的计算或在多个负载不确定性下的极限载荷。
This work proposes a novel theoretical framework of robust limit analysis i.e. the computation of limit loads of structures in presence of uncertainties using limit analysis and robust optimization theories. We first derive generic robust limit analysis formulations in the case of uncertain material strength properties. We discuss various ways of modeling uncertain strength properties and introduce the notion of robust strength criteria. We formulate static and adjustable robust counterparts of the corresponding uncertain limit analysis problems. Depending on the chosen strength uncertainty model, we also discuss tractable reformulations or approximations which can be implemented numerically using conic programming solvers. Building upon these results, we also derive robust limit analysis formulations in presence of loading uncertainties. Finally, various applications illustrate the versatility of the proposed framework including the derivation of a robust Mohr-Coulomb criterion with uncertain cohesion and friction angle, the computation of limit load of a structure subject to the partial loss of some components, or the limit load of a truss structure under multiple load uncertainties.
