A consistent equilibrium in a cross-section of an elastic-plastic beam
The authors deal with inequalities for stresses determined from equilibrium equations and those obtained from constitutive equations in cross-sections of beams and shells in the case of standard finite element formulations. Starting from the Reissner finite strain beam theory, the authors discuss in detail a phenomenon termed here as ``inconsistent equilibrium'' for a plane finite-strain elastic-plastic beam. The rotation of the centroid axis of the beam is considered as the only unknown function, and a balance function is introduced which ``measures'' the error. Numerical results are given in tables and diagrams for two finite element formulations for both consistent and inconsistent equilibria in cross-section.
plane finite-strain elastic-plastic beam
scientific article; zbMATH DE number 1342453