A semi-analytical approach for predicting the post-buckling response of laminates with a cutout

A semi-analytical solution method is developed For post-buckling analysis of moderately thick, flat composite laminates with a central elliptical cutout and subjected to general inplane loading. In order to help initiate the nonlinear post-buckling behavior in the panel, a small-magnitude initial geometric imperfection in the form of a one-term double sinusoidal function is included and directly invoked into the strain-displacement relations. The kinematics of the laminate is based on a {3,0}-higher order theory that provides a quadratic through-the-thickness variation of the transverse shear strains, thus producing the correct representation of the transverse strain energy of the laminate. The nonlinear Green strain-displacement relations are simplified by employing von Karman's assumptions. The present solution method utilizes the principle of virtual work in order to derive the nonlinear incremental equilibrium equations. The governing incremental equations are solved through an incremental iterative approach based on a Newton-Raphson algorithm. The validity of the present semi-analytical approach is established by comparison against measurements and finite element predictions for two different laminations subjected to uniform end displacement under compression and shear loading.