Flexural–torsional buckling loads for spatially coupled stability analysis of thin-walled composite columns

For the spatially coupled stability analysis of thin-walled composite beam with symmetric and non-symmetric laminations, the element stiffness matrix is presented using the technical computing program Mathematica. For this, the bifurcation type buckling theory of thin-walled composite beam subjected to an axial compressive force is developed by extending the nonlinear anisotropic thin-walled beam theory proposed by Bauld and Tzeng. From the stability equations, the explicit expressions for displacements are derived based on the displacement state vector consisting of 14 displacements, and then the element stiffness matrix is determined using the force–deformation relations. In addition, as a special case, the analytical solutions for buckling loads of the orthotropically laminated composite beams with various boundary conditions are derived. To demonstrate the validity and the accuracy of this study, the numerical solutions are presented and compared with the analytical solutions and the finite element results using the Hermitian beam elements and ABAQUS’s shell elements.