Plate-Bending Analysis by NURBS-Based Scaled Boundary Finite-Element Method

Abstract

This paper extends the idea of using nonuniform rational B-splines (NURBS) based shape functions in the scaled boundary finite-element method (SBFEM) to plate bending formulations, which inherits the advantages of the isogeometric analysis (IGA) as well as the scaled boundary finite-element method. The NURBS are introduced to reconstruct an exact boundary for analysis domain with arbitrary complicated geometry, h-, p-, and k- refinement strategies, which can maintain the same exact geometry as the computer-aided design (CAD) model at all levels. The NURBS basis functions are also used for the approximation of physical quantities inspired by the sense of isoparametric concept, and the high-order continuity of the NURBS basis functions contributes to the better accuracy, convergence, and efficiency of the present isogeometric scaled boundary finite-element method (IGSBFEM). The proposed technique is derived based on the exact three-dimensional elastic theory, which contributes to its high-accuracy property, whereas only discretization of the midplane is required for the present model due to the characteristics of dimensionality reduction and analytical property along the radial direction from the conventional SBFEM, and the solutions along the thickness direction are described as analytical expressions. Five numerical examples involving complicated geometries and multiconnected domains are carried out to examine the applicability of the present approach. Available solutions computed by several other methods (such as the analytic method, FEM, conventional SBFEM, and IGA) are used for comparison. Higher accuracy and efficiency compared with the traditional approaches are achieved.