THE PROBLEMS OF LIMIT LOAD ANALYSIS AND OPTIMIZATION USING EQUILIBRIUM FINITE ELEMENTS

Abstract

Summary The equilibrium dual discrete mathematical models of the problems of limit load analysis and optimization are investigated in the article. These models are presented in terms of static and kinematic formulation using equilibrium finite elements. In these mathematical models the possible discontinuities of displacement velocities are evaluated and the velocity of energy dissipation is estimated not only within the volume of finite elements, but at the plastic surfaces between elements. At first, on the basis of the energy principle of the maximum external power [1,2] the general mathematical models (3) and (7) of static formulation of limit load analysis and optimization problems are created. In these models the yield conditions are controlled not only within the volume, but also at the surfaces of finite elements. The equilibrium finite elements and interpolation functions of strains (9) are used for discretization of these models. The constancy of external power is taken as the optimum criterion....