Buckling and post-buckling analysis of the delaminated composite plates using the Koiter-Newton method

The Koiter-Newton method has been proved to be a computationally efficient method for buckling and post-buckling analysis of structures, using a novel reduced-order modeling strategy. In this paper, the existing method is extended for laminated composite plates with delamination. We develop a 4-node quadrilateral element S4DE as a geometric linear element in the co-rotational formulation of the Koiter-Newton method. The assumed layerwise displacement model of the developed element is enriched with Heaviside unit step functions to model delamination. The displacement fields of each layer are described using the superposition of first-order shear deformation and layerwise functions. The zig-zag theory is applied to enhance the numerical accuracy and computational efficiency of the developed element. The construction of the reduced order model requires derivatives of the strain energy with respect to the degrees of freedom up to the fourth order, which is two orders more than traditionally needed for a Newton based nonlinear finite element technique. The geometrical nonlinearities are taken into account using derivatives of the local co-rotational frame with respect to global degrees of freedom. Various laminated plates with different thicknesses, delamination lengths and stacking sequences are considered to validate the good performance of the present method in terms of numerical reliability, accuracy and computational effort.