A robust frame element with cyclic plasticity and local joint effects

A robust elasto-plastic element is developed for analysis of frame structures. The element consists of a beam member with end joints with properties permitting representation of the effect of section forces in adjoining members, like axial forces. By use of the equilibrium formulation the deformations of beam member, plastic hinges and joints become additive and can be expressed in explicit form. The plastic deformations of the beam and the joints are represented by separate plastic mechanisms, described by the same generic cyclic plasticity format. This format is defined by an energy function, a yield surface, and a plastic flow potential for each plastic mechanism. In the cyclic plasticity model each component is characterized by the elastic stiffness, the yield capacity, the additional flexibility at initial yield, the ultimate capacity and a shape parameter describing the curvature of the hysteresis curve. The yield surface is represented by a recently developed generic format, combining the section forces into a homogeneous function of degree one and permitting smooth transition between regions with large and more moderate curvature. A robust return algorithm of approximately second order is developed, using a mid-step state to obtain representative information about the return path. The element is implemented in a co-rotational large-deformation computer program for frame structures. The formulation is illustrated by application to a couple of typical offshore frame structures, and comparison of different representations of the plastic effects illustrates the importance of a robust element with realistic representation of the cyclic plastic mechanisms.