A complex potential-variational formulation for buckling analysis of flat laminates with multiple cutouts

A semi-analytical method is developed for pre-buckling and buckling analyses of thin, symmetrically laminated composite panels containing multiple elliptical cutouts at arbitrary locations and orientations under general combined loading conditions. Both the pre-buckling and buckling analyses are based on the variational method in conjunction with complex functions. The complex potential functions in the pre-buckling state automatically satisfy the in-plane stress equilibrium equations, thus reducing the computation of the first variation of the total potential energy to line integrals only. Because the complex potential function for out-of-plane displacement is augmented by complete polynomials, the area integral terms in the second variation of the total potential energy, referred to as the Treftz criterion, are retained in the buckling analysis. These complete polynomials improve the global buckling response of the panel while the complex potential functions associated with each cutout capture the local buckling response of the panel. Lagrange multipliers with unknown coefficients are introduced in functional forms in order to satisfy the kinematic boundary conditions.