Large-Displacement Analysis of Elastoplastic Thin-Walled Frames. I: Formulation and Implementation

Abstract

This paper presents a new formulation for the large-displacement analysis of thin-walled frames taking into account the effects of elastoplastic material behavior. The proposed formulation is derived in an Eulerian (convected) local system which allows relatively simple strain-displacement relationships to be used. Furthermore, the formulation uses the fiber approach for representing the spread of plasticity over a general open cross section, and is capable of modeling initial imperfections, residual stresses, and the Wagner effect. In accounting for material plasticity effects, consideration is given to the interaction between normal stresses and shear stresses due to twisting. Since the shear strain is directly related to the rate of twist, the shear stress in the yield function is replaced by an equivalent contribution to the cross-sectional torque, which leads to considerable computational advantages. This paper describes the formulation details and the implementation of material plasticity effects for kinematic and isotropic strain hardening, whereas the companion paper provides a number of verification and application examples.