Finite element formulations for thin -walled members

Conventional solutions for the equations of equilibrium based on the well known Vlasov thin-walled beam theory uncouple the equations by adopting orthogonal coordinate systems. This technique introduces several modeling complications and limitations where eccentric supports or abrupt cross-sectional changes exist (in elements with rectangular holes, coped flanges, or longitudinal stiffened members, etc.).;The shear deformation effect due to warping torsion is included in the torsional analysis of open thin-walled beams of general cross-section. The principle of stationary complementary energy is adopted to formulate the governing field compatibility condition. The variational principle is then extended to formulate a finite element, which captures shear deformation effects and allows the use of a minimal number of elements. For squat beams, shear deformation effects are shown to gain significance.;Field equations and boundary conditions are obtained for the buckling analysis of thin-walled members by using the principle of stationary complementary energy. Subsequently a finite element is derived which incorporates shear deformation effects, a feature that is neglected in most available buckling solutions. It is shown that conventional solutions which neglect shear deformation effects can overestimate the predicted buckling load in some cases. The proposed finite element formulation can be used for the problems of column flexural buckling and torsional buckling, as well as beam lateral torsional buckling under linear moment gradients for doubly symmetric, mono-symmetric and channel sections. By adopting a non-orthogonal coordinate system, the solution is able to successfully capture load position effects relative to the shear centre. The efficiency and availability of the formulation is shown through comparisons to results based on shell finite element analysis solutions and other closed form or numerical solutions in the literature.;In this study, a general solution of the Vlasov thin-walled beam theory based on a non-orthogonal coordinate system is developed. A finite element formulation, which yields nodal values in exact agreement with those based on the closed form solution of the Vlasov field equations and boundary conditions, is derived. The advantages and modeling capabilities of the formulation are discussed in detail. General expressions for normal and shearing stresses under non-orthogonal coordinate systems are developed. For design purposes, an elastic interaction equation for general open thin-walled section is derived.