Multi-criteria Estimation of Load-Bearing Capacity of Solids

Abstract

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.