The article discusses the problem of the load-bearing capacity of a deformable solid in the current configuration, which may be either reference (undeformed) or actual (deformed). An original variational approach is proposed, where, depending on different engineering considerations, the root-mean-square values (rms) of any stress components in various sub-domains are calculated and used to estimate the load-bearing capacity of the current configuration of a solid for given loads. For example, an estimate of the rms value of hydrostatic pressure is necessary for analyzing the load-bearing capacity of concrete. On the other hand, the rms value of all stress components in the vicinity of a concentrator (a neck or a groove) makes it possible to estimate the overall strength of a sample in full-scale rupture experiments. The proposed approach differs fundamentally from the classical rigid-plastic analysis of the load-bearing capacity of the reference configuration of a solid, within which a point criterion for the maximum intensity of tangential stresses or the local strain energy density is used. One of the drawbacks of rigid-plastic analysis is the uncertainty of the stress field in the rigid sub-domains of a solid. This effect is not present in the proposed method of assessment. The article provides informative and straightforward analytical and numerical examples showing the non-triviality of the proposed methodology.

中文翻译：

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固体承载力的多准则估计

文章讨论了可变形实体在当前配置中的承载能力问题，可以是参考（未变形）或实际（已变形）。提出了一种原始的变分方法，根据不同的工程考虑，计算各个子域中任何应力分量的均方根值 (rms) 并用于估计当前配置的承载能力给定载荷的固体。例如，静水压力的均方根值的估计对于分析混凝土的承载能力是必要的。另一方面，集中器（颈部或凹槽）附近所有应力分量的均方根值可以在全尺寸破裂实验中估计样品的整体强度。所提出的方法从根本上不同于固体参考配置承载能力的经典刚塑性分析，其中使用切向应力的最大强度或局部应变能密度的点标准。刚塑性分析的缺点之一是固体刚性子域中应力场的不确定性。这种影响在建议的评估方法中不存在。文章提供了信息丰富且直接的分析和数值示例，显示了所提出方法的重要意义。其中使用切向应力的最大强度或局部应变能密度的点准则。刚塑性分析的缺点之一是固体刚性子域中应力场的不确定性。这种影响在建议的评估方法中不存在。文章提供了信息丰富且直接的分析和数值示例，显示了所提出方法的重要意义。其中使用切向应力的最大强度或局部应变能密度的点准则。刚塑性分析的缺点之一是固体刚性子域中应力场的不确定性。这种影响在建议的评估方法中不存在。文章提供了信息丰富且直接的分析和数值示例，显示了所提出方法的重要意义。