Extended isogeometric analysis based on Bézier extraction for the buckling analysis of Mindlin–Reissner plates

Abstract

In this paper, the buckling analysis for the Mindlin–Reissner plates is performed by applying the isogeometric analysis (IGA) coupled with Bezier extraction operator. The Bezier extraction operator allows the incorporation of non-uniform rational B-spline-based IGA into the existing finite element method (FEM) work frame. For cracked plates, the extended IGA (XIGA) is employed. Unlike previous FEM approaches, the present method is expected to be more accurate and to achieve higher convergence as the polynomial order increases. A discrete shear gap is applied to address shear locking. The results obtained by the present method for the plates with and without crack are compared with the reference solutions. It is found that the present method possesses the following desirable properties: (i) the simulation results are found to be in good agreement with the reference solutions; (ii) the present method is able to preserve the exact geometry of complicated surfaces; and (iii) the method can be applicable to both moderately thick and thin plates straightforwardly. The effects of various plate shapes, side-to-thickness ratio, aspect ratio, crack length, and boundary conditions are also studied.