Buckling of thin-walled open beams including warping and shear deformation

The aim of the present study is to present the geometric stiffness matrix of thin-walled open beams with an arbitrary cross-section. This element takes into account the effects of flexural sheer deformations and warping deformations. The usage of an orthogonal Cartesian coordinate system obviates the Lid hoc introduction of St. Venant stiffness. The principle of virtual work in an updated Lagrangian procedure has been used to derive the geometric stiffness. The resulting linearized buckling problem is solved by the inverse iteration with shift. A buckling problem is presented to demonstrate the convergence and accuracy of the new finite element.