A co-rotational finite element with embedded plastic discontinuities consistently accounting for distributed loads

Abstract

Abstract A co-rotational model with distributed loads is employed to analyze planar frames considering plasticity effects lumped by means of embedded discontinuities. The model consistently accounts for the influence of distributed loads into the tangent stiffness matrix, which appears in the co-rotational description of motion. The element is locally formulated as the traditional linear Euler-Bernoulli element. The plastic embedded discontinuities are introduced into the generalized strains fields by Dirac deltas centered at the element ends, naturally resulting in the lumped plasticity local element formulation. The global nonlinear equilibrium equations are solved by either force- or displacement-control Newton based procedure, depending on the observed snaping phenomena. On the other hand, the plastic constrained nonlinear system of equations related to the local problems is solved with a Newton-Raphson approach, running through all feasible plastic possibilities. Both the stiffness and local problem tangent matrix are explicitly presented. Four examples are presented to demonstrate the robustness of the formulation to deal with elastoplastic nonlinear analysis of frames.