Large rotations elastic buckling analysis of thin-walled beam structures

in this paper a numerical analysis of thin-walled beam structures, based on the finite element method, is presented. The finite clement equation is derived by using the linearized virtual principle under assumptions of large displacements, small strains, isotropic and linear elastic material, internal moments are calculated by engineering theories. Linear shape functions are used for the axial displacement, while cubic shape functions are employed for transverse displacements and angle of twist. Also, by using a non-linear displacement field of cross-section that includes the large rotation effect, the geometric stiffness matrix of thin-walled beam finite element is derived, in which internal moments are obtained as semitangential. In the case of quazitangential external moments corresponding correction stiffness matrices are as well derived. The accuracy of presented numerical algorithm is examined Throughout the test problems.