Exact lateral buckling analysis for thin-walled composite beam under end moment

An improved numerical method to evaluate exactly the element stiffness matrix is proposed for the lateral buckling analysis of thin-walled composite I- and channel-section beams with symmetric and arbitrary laminations subjected to end moments. For this, the bifurcation type buckling theory of thin-walled composite beams subjected to pure bending is developed based on the energy functional. Stability equations and force–deformation relationships are derived from the energy principle and explicit expressions for displacement parameters are derived based on power series expansions of displacement components. Then the exact element stiffness matrix is determined using force–deformation relationships. In addition, analytical solutions for lateral buckling moments of unidirectional and cross-ply laminated composite beams with various boundary conditions are derived, as a special case. Finally, the finite element procedure based on Hermitian interpolation polynomials is developed. In order to verify the accuracy of this study, numerical solutions are presented and compared with the analytical solutions and the finite element solutions using the Hermitian beam elements, ABAQUS’s shell elements and the results by other researchers. Also, the effects of fiber orientation and the Wagner effect on the lateral buckling moments are studied.