Двойственные вариационные постановки задач деформируемого тела при разрывных полях перемещений

Abstract

There are created the dual variational formulations of the stress-strain field analysis and optimization problems of the elasto-plastic body with displacement discontinuity in case monotonically increasing (simple) loading. These formulations allow to create various schemes of finite elements in the plasticity theory. Displacement discontinuities in dual formulations of problems are estimated by yield conditions in the places of these discontinuities (surfaces of finite elements). The relations of variational principles and problems of deformable body with displacement discontinuities and some them transformations is shown. The extremum principle of Haar-Karman, Colonnetti, Prager-Symonds, Castigliano and the energy principles (static theorems) of ideal rigid-plastic body’s limit state analysis are received from the principle of a minimum total complementary energy. The principles of Greenberg, Lagrange and the kinematic theorems about the limit load and the simple plastic failure are received from the elasto-plastic body’s principle of a minimum total deformations energy.