Delamination analysis of laminated composite shells is studied. For this purpose, a four-noded flat shell element for linear and geometrically non-linear analyses is developed. The formulation is based on a first-order shear deformation theory (FSDT) and is valid for large displacements but moderate rotations. The extended finite element method (XFEM) is used to impose the discontinuous domain at an arbitrary through-the-thickness location. The progressive failure at the interface region is simulated through a mixed-mode cohesive zone model based on an exponential softening behavior. In addition, a simple non-frictional contact formulation is utilized to avoid the penetration of the discontinuous subdomains. To diminish the instability problem of the interface formulation, different integration rules are taken into account. Furthermore, the arc-length method with full Newton-Raphson iteration technique is applied to solve the non-linear governing equations. In order to verify the accuracy of the predictions, standard benchmark tests are carried out for analyzing shells, delamination, and the delamination buckling problems. The proposed model can be effectively used to model the delamination onset and its propagation in shell structures with less computational cost.
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