A co-rotational finite element formulation for buckling and postbuckling analyses of spatial beams

A consistent co-rotational finite element formulation and numerical procedu re for the buckling and postbuckling analyses of three-dimensional elastic Euler beam is presented. All coupling among bending, twisting, and stretchi ng deformations for a beam element is considered by consistent second-order linearization of the fully geometrically nonlinear beam theory. However, t he third-order terms, which are relevant to the twist rate and curvature of the beam axis, are also considered. An incremental-iterative method based on the Newton-Raphson method combined with constant are length of increment al displacement vector is employed for the solution of nonlinear equilibriu m equations. The zero value of the tangent stiffness matrix determinant of the structure is used as the criterion of the buckling state. A bisection m ethod of the are length is proposed to find the buckling load. Numerical ex amples are presented to demonstrate the accuracy and efficiency of the prop osed method and to investigate the effect of third-order terms on the buckl ing load and postbuckling behavior of three-dimensional beams. (C) 2000 Els evier Science S.A. All rights reserved.