A finite element complementary energy formulation for plane elastoplastic stress analysis

Abstract

The m.ethod of analysis presented herein parallels that of Ref (8) with two added major distingushing features. First, the present model consists of an eighteen degree of freedom self-equilibrating finite element model wherein the stress function is expressed by means of a complete set of quintic Hermitian polynomials. The function used, while allowing for selfequilibrating stresses that are continuous within the element, also enables the admission of all the second derivatives of the function as nodal parameters, thereby permitting the determination of nodal stress values directly without the need of additional computation. Second, the present work introduces an additional force parameter that is essential to satisfy complete static equilibrium of external forces constistent with the assumed stress function.