Evaluation of bearing capacity of a beam on an elastic foundation using the methods of the theory of limiting balance

The analytical expressions and graphs for determining a limiting load have been obtained using the methods of the theory of limiting balance. The processes of strain of the beams after formation of a plastic hinge until their complete destruction have been investigated. The dependences of a bearing capacity of the beam on its parameters and characteristics of the foundation soils have been obtained. The regularities of formation of plastic hinges have been revealed depending on a place of application of the load. The limiting values of the load have been calculated analytically, and the forms of deformation of the beam have been established at the time of the appearance of the first plastic strains and in the limiting state. The comparative analysis of the research results of the adopted model with the numerical studies of the elastoplastic beam has been carried out.

Collapse Analysis of Ship Hull Girder Using Hydro-Elastoplastic Beam Model: Part 2

In Part 1 study, a time-domain collapse analysis method of ship hull girder was developed and named FE-Smith method. Hull girder was treated as elastoplastic beam model and Smith’s method was used for collapse analysis of cross sections. A concept of average stress-average plastic strain relationship was introduced so that nonlinear collapse behavior of members can be treated as pseudo strain-hardening/softening behavior. Fluid-structure interaction effects were considered. Uniform cross-section beam was assumed as a most fundamental study. In this Part 2, a container ship is taken as subject model. Not only FE-Smith analysis but also non-linear FE analyses using shell model for collapse parts are performed for comparison purpose. Two types of average stress-average strain curves are considered for FE-Smith analysis, i.e. obtained by Gordo-Soares formulae and by shell FEM. Applicability of FE-Smith method is examined comparing with more precise but time-consuming methods. Some parametric studies are also performed. Wave response will be reported in the next papers.

Fatigue and phase transition in an oscillating elastoplastic beam

We study a model of fatigue accumulation in an oscillating elastoplastic beam under the hypothesis that the material can partially recover by the effect of melting. The model is based on the idea that the fatigue accumulation is proportional to the dissipated energy. We prove that the system consisting of the momentum and energy balance equations, an evolution equation for the fatigue rate, and a differential inclusion for the phase dynamics admits a unique strong solution.

Elasto-Plastic Beam Afloat on Water Subjected to Waves

This paper addresses development of a mathematical model which describes the behavior of an elasto-plastic beam afloat on water surface. The mathematical model is valid for predicting the collapse of a Very Large Floating Structure (VLFS) subjected to extreme wave-induced vertical bending moment. It is a follow-up of the previous work in which the collapse behavior of a VLFS is pursued by adopting a segmented beam approach. In this research, the whole VLFS is modelled with elasto-plastic beam elements. The hydrodynamic behavior is modeled by using Rankine source panel method based on time-domain potential theory. It is shown that the elasto-plastic beam approach gives almost the same result as the segmented beam approach for predicting the one-element collapse behavior. The elastoplastic beam approach is extensively used to predict the progressive collapse spread over multiple sections, which cannot be followed by the segmented beam approach.