Buckling Solution of Fixed-Free Anisotropic Laminated Composite Columns Under Axial Loading

A generalized buckling solution for anisotropic laminated composite fixed-free columns under axial compression is developed using the critical stability matrix. The axial, coupling, and flexural equivalent stiffness coefficients of the anisotropic layup are determined from the generalized constitutive relationship through the static condensation of the composite stiffness matrix. The derived formula reduces down to the Euler buckling equation for isotropic and some special laminated composites. The analytical results are verified against finite element solutions for a wide range of anisotropic laminated layups yielding high accuracy. A parametric study is conducted to examine the effects of ply orientations, element thickness, finite element type, column size, and material properties. Comparisons with numerical results reveal a very high accuracy across the entire parametric profile and a linear correlation between the percentage error and a non-dimensional condensed parameter is extracted and plotted.