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 elasto-plastic material behaviour. The proposed formulation is derived in an Eulerian (convected) local system which allows relatively simple strain-displacement relationships to be used. Furthermore, the formulation employs the fibre approach for representing the spread of plasticity over a general open cross-section, and is capable of modelling 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. The present 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.

A 3-Node Co-Rotational Triangular Elasto-Plastic Shell Element Using Vectorial Rotational Variables

“…In addition, the residual bending flexibility is added to the transverse shear flexibility to improve the accuracy of the element further. For elasto-plastic modeling, the fibre approach which can describe the plastic zone spreading process in shell structures undergoing large elastoplastic deformation [56][57][58][59] is adopted, the Maxwell-Huber-Hencky-von Mises yield criterion for isotropic hardening case [60][61][62][63][64] is introduced, and the material is assumed to be linear hardening. A backward-Euler return-mapping integration algorithm [60][61] is used to trace the yield surface, and a consistent elasto-plastic tangent modulus matrix is employed.…”

“…For elasto-plastic modeling, the fibre approach which can describe the plastic zone spreading process in shell structures undergoing large elastoplastic deformation [56][57][58][59] is adopted, the Maxwell-Huber-Hencky-von Mises yield criterion for isotropic hardening case [60][61][62][63][64] is introduced, and the material is assumed to be linear hardening. A backward-Euler return-mapping integration algorithm [60][61] is used to trace the yield surface, and a consistent elasto-plastic tangent modulus matrix is employed. To exclude the influence of element rigid-body rotations from the local displacement field, a zero-'macro spin' co-rotational framework, which can significantly reduce the rigid-body rotations of infinitesimal segments at different material points within the element domain in an aggregate sense [65], is employed for the present element to simplify the stress-strain constitutive relation.…”

Conceptual issues in geometrically nonlinear analysis of 3D framed structures

“…Two alternative definitions of global rotations are considered in the variant approaches: the first is based on a resultant rotation vector [8], whereas the second employs modified Euler angles [10]; accordingly, T r is dependent on the variant approach as detailed later. The rotational transformation matrices at the two element nodes determine the current cross-sectional orientation vectors ( (13) in which, in (13) is a fictitious vector used for the evaluation of the element twist rotation [8], as demonstrated later.…”

“…For practical small strain problems, the local deformations ( u c ) can be assumed to be small, with this assumption becoming increasingly justified as more elements are used per member [13]. The global nodal displacements combined with c …”

Bars under Torsional Loading: A Generalized Beam Theory Approach

“…Wunderlich et al [124] employed a power series numerical technique using an Updated Lagrangian formulation to study thin-walled beams under general loading conditions. Izzuddin and Lloyd Smith [125,126] followed an Eulerian approach employing cubic shape functions to study thin walled bars under general loading conditions. Chen and Trahair [99] and Pi and Trahair [121], using a mitre model [127] to describe the shear strain distribution over the cross section, developed finite element models for the inelastic analysis of thin-walled I-beams under torsion.…”