DUAL MATHEMATICAL MODELS OF ELASTOPLASTIC STRUCTURES ANALYSIS PROBLEM ESTIMATING DISCONTINUITY OF DISPLACEMENTS

Abstract

A problem of ideal elastoplastic structures stress-strain field determination is considered in the article. The general dual mathematical models (static and kinematic formulation) of analysis problem is derived on the basis of the extremal energy principles and theory of duality. The different external effects are estimated, namely: load, initial strains, prestressing and support settlements. At first, on the basis of the complementary energy principle the mathematical model of static formulation of the problem is made. The kinematic formulation of the problem is obtained on the basis of Lagrange's multipliers method; this corresponds to the minimum total energy principle for a kinematically admissible displacements. In these mathematical models the possible discontinuity of displacements and the dissipation of energy in the place of those discontinuities are estimated what was not done in the previous publications. The discrete expressions of fundamental relationships (equilibrium and geometric equations, yield conditions) and a dual pair of discrete equilibrium mathematical models are obtained on the basis of general static formulation of the problem using equilibrium finite elements. They permit to determine the upper meanings of the stress and displacements of structures. In the article it has been shown, that the approximation of yield conditions by Bubnov-Galiorkin's collocation method gives the more accurate results.