Buckling and post-buckling analysis of cracked stiffened panels via an X-Ritz method

A multi-domain eXtended Ritz formulation, called X-Ritz, for the analysis of buckling and post-buckling of stiffened panels with cracks is presented. The theoretical framework is based on the First-order Shear Deformation Theory and accounts for von Kármán's geometric nonlinearities. The structure is modeled as assembly of plate elements. Penalty techniques are used to fulfill the continuity condition along the edges of contiguous elements and to satisfy essential boundary conditions requirements. The use of an extended set of approximating functions allows to model through-the-thickness cracks and to capture the crack opening and tip singular fields as well as the structural behavior within each single domain. Numerical results for buckling and post-buckling of cracked stiffened panels are compared with finite elements simulations and literature solutions, showing the accuracy and potential of the proposed approach.