Preisach Model for Cyclic Bending of Elastoplastic Beams

Abstract

In the present paper, the Preisach model, already successfully implemented for the problem of axially loaded members, has been extended to the cyclic bending of elasto-plastic beams. Starting from Hooke's and St. Venant's element, very well known in the theory of plasticity, using the Preisach model the stress at an arbitrary fiber of the cross section, and at an arbitrary instant of time can be found for a precribed history of curvarure change. The solutions for pure bending of symmetrical cross sections (rectangular and I-section) are presented. Also pure bending of an unsymmetrical (triangular) cross section, and the bending of a symmetrical (rectangular) cross section due to the simultaneous action of axial stretching of the neutral fiber and curvature change are considered.