Co-rotational formulation for geometric nonlinear analysis of doubly symmetric thin-walled beams

✍ Scribed by Wen Yi Lin; Kuo Mo Hsiao

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 397 KB
• Volume: 190
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(01)00212-2

✦ Synopsis

A doubly symmetric thin-walled beam element with open section is derived using co-rotational (CR) total Lagrangian (TL) formulation. The eects of deformation-dependent third-order terms of element nodal forces on the buckling load and post-buckling behavior are investigated. All coupling among bending, twisting, and stretching deformations for beam element is considered by consistent second-order linearization of the fully geometrically nonlinear beam theory. However, all third-order terms of nodal forces, which are relevant to the twist rate, rate of twist rate and curvature of the beam axis are also considered. An incremental-iterative method based on the Newton±Raphson method combined with constant arc length of incremental displacement vector is employed for the solution of nonlinear equilibrium equations. The zero value of the tangent stiness matrix determinant of the structure is used as the criterion of the buckling state. A parabolic interpolation method of the arc length is used to ®nd the buckling load. Numerical examples are presented to demonstrate the accuracy and eciency of the proposed element and to investigate the eect of third-order terms of element nodal forces on the buckling load and post-buckling behavior of doubly symmetric thin-walled beams.