Spatial Postbuckling Analysis of Nonsymmetric Thin-Walled Frames. II: Geometrically Nonlinear FE Procedures

In a companion paper, transformation rules of Rodriguezʹ finite rotations and semitangential rotations are derived, respectively, and their rotational properties are discussed. The shear deformable displacement field of nonsymmetric thin-walled space frames is introduced based on semitangential rotations and the potential energy corresponding to semitangential internal moments are consistently derived using the proposed displacement field. In this paper, for spatial postbuckling analysis of thin-walled space frames, the elastic strain energy including bending-torsion coupled terms and shear deformation effects is derived using transformations of displacements and stress resultants defined at the centroid and the centroid-shear center, respectively. Tangent stiffness matrices of the frame element are derived by using Hermitian polynomials including shear effects, and an improved corotational formulation is presented by separating rigid body motions and pure deformations from incremental displacements, calculating the corresponding generalized forces and updating direction cosines of frame elements. In addition, a scheme to evaluate load correction stiffness matrices due to the off-axis loading and conservative moments is addressed. FE solutions for the postbuckling are presented and compared with results by ABAQUS shell models.