Stability of shear deformable thin-walled space frames and circular arches

A consistent finite-element formulation is presented in order to analyze the spatial stability of shear deformable thin-walled space frames and circular arches. The displacement field of unsymmetric thin-walled cross sections is introduced based on the inclusion of second-order terms of Rodriguez's finite rotations, and the potential energy corresponding to the semitangential moments is consistently derived. For finite-element analysis, cubic Hermitian polynomials including shear deformation effects due to flexural and restrained warping shear stress are utilized as shape functions. Load correction stiffness matrices for the different types of moments and off-axis loadings are taken into account. For spatial buckling behaviors of space frames and circular arches, finite-element solutions using the two-noded straight frame element are presented and compared with the analytical solutions and the results in the literature.