Postbuckling analysis of multi-directional perforated FGM plates using NURBS-based IGA and FCM

Geometric modeling and numerical analysis of multi-directional FGM (Functionally Graded Material) plate, whose material properties grade continuously both in its thickness and in-plane directions, are increasingly required. In this work, postbuckling behavior of this type of plates with multiple cutouts is, for the first time, numerically investigated through the combination of NURBS-based IGA (IsoGeonetric Analysis) and FCM (Finite Cell Method). The nonlinear deformation of plate is determined by TSDT (Third-order Shear Deformation Theory) and von Kármán nonlinear assumptions without the requirement of SCFs (shear correction factors). Besides, the higher continuity advantage of NURBS basis functions can easily meet the C¹-continuous requirement of the displacement field. The main contribution is introducing the FCM to deal with the influence of complex cutouts on the postbuckling characteristics. The geometric interfaces of the cutouts are approached and approximated by adaptive quadrature procedure in the distinguished cut elements. The advantage of this implementation is that the previously tricky process of representing the geometry of perforated plate with multiple NURBS patches can be eliminated, which naturally avoids the imposition of C¹-continuity condition across the patch boundaries. The cylinder arc-length method combined with modified Newton–Raphson iteration algorithm, which takes into account of the initial geometric imperfections, is applied to implement geometrically nonlinear stability analysis and track the postbuckling paths. The effectiveness and reliability of the presented method are verified with available solutions of isotropic and conventional perfect FGM plates. Subsequently, a series of factors, including material volume fraction, length-to-thickness ratio, boundary condition, cutout size, etc., affecting the postbuckling responses of multi-directional perforated FGM plates are considered and investigated.