Large elastic-plastic deformations of slender beams: Co-rotational theory vs. von Karman theory

Abstract

The consistent co-rotational beam formulation has been modified to include inelastic deformation using a sublayer material model. An explicit tangent stiffness matrix for a non-conservative beam was consistently derived from the assumed beam kinematics. Several example problems were solved to verify the formulation and, subsequently, a comparative study was carried out to examine the validity of the von Karman theory in large deflection analysis. It is found that the presence of beam axial constraint plays an important role on the performance of the von Karman approximation. In general, the von Karman formulation can provide reasonable solutions to large deformation problems of extensional structures, but its performance becomes unsatisfactory for the inextensional case even under relatively small deflections.