LAUSR

Abstract This work is devoted to numerical investigation for buckling of functionally graded plates (FGPs) with internal holes using an efficient adaptive isogeometric analysis (IGA). The locally refined (LR) B-splines, which possess the local refinement ability, are used as basis functions in IGA. Kinematics of plate structures are derived using the simple quasi-3D hyperbolic shear deformation theory (S-Q3HSDT), which has few unknowns, free from shear locking, and suitable for considering the shear deformation and thickness-stretching effect. The high-order continuity of LR B-splines directly meets the requirement of C 1 -continuity in the S-Q3HSDT. Internal holes are described by the level set method, and the physical mesh is independent of the hole boundaries. Local refinement is guided by a posterior error estimation based on strain recovery of the first buckling mode and the structural mesh refinement strategy. Several numerical examples considering different types of cutouts are studied, and the computed results are compared with reference solutions available in the literature to show the accuracy and performance of the developed method. The present method automatically identifies the required local refinement zones, improves the computational accuracy at a low cost, possesses high convergence speed, and avoids the usage of trimmed surfaces in the analysis. The effects of boundary condition, hole shape, hole size, load direction, and multiple holes on the buckling behavior of FGPs are investigated in detail.