A consistent finite element formulation for linear buckling analysis of spatial beams

Abstract

A consistent co-rotational finite element formulation and numerical procedure for the linear buckling analysis of three-dimensional elastic Euler beam is presented. A mechanism for generating configuration dependent conservative moment is proposed and the corresponding load stiffness matrix is derived. It is assumed that the prebuckling displacements and rotations of the structure and the corresponding deformations of the elements are linearly proportional to the external loading. The prebuckling rotations of the structure are fixed axis rotations or small rotations, and the effect of the prebuckling displacement on transformation matrix for the coordinates transformation can be ignored. All coupling among bending, twisting and stretching deformations for beam element is considered by consistent linearization of the fully geometrically nonlinear beam theory. An inverse power method for the solution of the generalized eigenvalue problem is used to find the buckling load and buckling mode. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method. (C) 1998 Elsevier Science S.A.