A GEOMETRICALLY EXACT THIN-WALLED BEAM THEORY CONSIDERING IN-PLANE CROSS-SECTION DISTORTION

Abstract

A fully nonlinear theory of a three-dimensional thin-walled beam, in arbitrary rectangular coordinates with the pole of the sectorial area at an arbitrary point and the origin of the sectorial area at an arbitrary point of the beam section, is developed to incorporate transverse shear, torsion-induced warping, and local-buckling-induced cross-section distortion. Based on a geometrically-exact description of the kinematics of deformation, this theory allows large deformation and large overall motion with a general out-of-plane warping function and a general in-plane distortion function. The present theory can exactly reduce to the classical Vlasov theory for vanishing shearing and cross-section distortion in the case of small deformation. The nonlinear weak form of the governing equations of equilibrium is constructed and the linearization of the weak form is derived. A finite element code is developed to implement this generalized thin-walled beam element. The results given by the post-buckling analysis are compared with numerical and/or experimental results to investigate the local buckling effect on the member behavior.