An Inelastic Finite Displacement Formulation of Thin-Walled Members

Abstract

The stiffness equation of linearized finite displacements for straight thin-walled members with inelastic material is derived. An arbitrary orthogonal coordinate system with a single reference point across the section need be introduced in the formulation, which is a clear distinction from the elasticity problem. Also distinct from the elastic analysis is a need to evaluate the magnitude of strains from time to time because of the dependence of the tangent modulus on strain levels. Illustrative examples are given to demonstrate the proposed method for the inelastic finite displacement analysis of spatial thin-walled members, with a simplified consideration on the effect of shear stresses.

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

“…Conci and Gattass (1990-b) adopted a plastic-hinge approach and commented on the difficulty of establishing the yield condition as a relationship between generalised cross-sectional stresses. Hasegawa et al (1987) considered plasticity in terms of material stresses, although the interaction between shear and normal stresses was simplified by the assumption that the tangent shear modulus is proportional to the normal tangent modulus. The most recent and complete work is that of Pi and Trahair (1994), where a Total Lagrangian approach was used, and a von Mises interaction with isotropic work hardening was assumed between the shear and normal stresses in the plastic range.…”

Dynamic stability of thin-walled composite beams under periodic transverse excitation

“…However, many of these theories differ in the order of nonlinearity considered in their formulation. For example, second-order displacement field has been used in a formulation of finite element models for 3-D nonlinear analysis of beam structures [29][30][31]. This approximation presents several advantages because it simplifies the coupling between the displacement and rotations and so the tangent stiffness matrix (used for the nonlinear incremental-iterative analysis) can be simplified.…”

Non-linear buckling and postbuckling behavior of thin-walled beams considering shear deformation

“…There are several studies based on the finite element method, Bazant and Nimeiri [5] developed a general stiffness analysis of spatial large deflections and postbuckling behavior of thin-walled members of asymmetric open cross-section. Bathe and Bolourchi [6], Yang and McGuire [7], Hasegawa et al [8], Kitipornchai et al [9] and Chen and Blandford [10] carried out studies of large deflections in beams using an updated Lagrangian procedure. A consistent co-rotational total Lagrangian formulation was presented by Hsiao and Lin [11][12][13] in the geometrically non-linear analysis of mono-and bi-symmetric beams.…”