Investigation of buckling characteristics of cracked variable stiffness composite plates by an eXtended Ritz approach

Variable Angle Tow (VAT) composite plates are characterized by in-plane variable stiffness properties, which opens to new concepts of stiffness tailoring and optimization to achieve higher structural performance for advanced lightweight structures where damage tolerance consideration are often mandatory. In this paper, a single-domain eXtended Ritz formulation is proposed to study the buckling behaviour of variable stiffness laminated cracked plates. The plate behaviour is described by the first order shear deformation theory whose generalized displacements, namely reference plane translations and rotations, are expressed via suitable admissible trial functions. These consist of a set of regular terms, built using orthogonal polynomials, augmented with special functions able to describe the crack opening and the singular behaviour at the crack tips; boundary functions are used to ensure the required homogeneous essential boundary conditions. Governing equations are inferred via the stationarity of the energy functional an solved to carry out an extensive study on the buckling behaviour of variable angle tow homogeneous and layered composite plates. The results obtained for homogeneous plates evidence that the crack presence strongly influences the buckling behaviour depending on its length and inclination and plate boundary conditions with a meaningful variability with respect to the fibre paths configuration, which can arrange for better performances with respect to the straight fibre case. Also for cracked laminates the results show that there are several fibre path able to provide higher buckling loads and higher overall axial stiffness with respect to the straight fibre case. In the framework of damage tolerant engineering applications, this allows to select fibre paths that guarantee predefined design levels of buckling load and axial stiffness even in presence of cracks. Finally, this study highlights the potential of the proposed approach for the analysis of the buckling behaviour of cracked composite variable stiffness plates, which provides an efficient analysis tool for the damage tolerant design and optimization of advanced variable stiffness structures.