A novel isogeometric scaled boundary finite element method for bending and free vibration analyses of laminated plates with rectilinear and curvilinear fibers constrained or free from elastic foundations

Abstract

In this paper, a novel numerical approach based on isogeometric analysis and the scaled boundary finite element method is performed, focusing on improving the computing performance (such as accuracy, efficiency and flexibility) of bending and free vibration analyses for laminated composite plates with rectilinear and curvilinear fibers constrained or free from elastic foundations. The non-uniform rational B-splines are used as shape functions for both the construction of exact geometry and the approximation of field variables. The governing formulations are derived from the 3D theory of elasticity, while only discretization for the 2D in-plane dimension is required, with the displacement and stress fields expressed analytically along the thickness direction. Compared to traditional methods, the proposed method possesses the following major advantages: a) The powerful calculation accuracy and less computation consumption due to the higher-order continuity of non-uniform rational B-splines and the intrinsic semi-analytical property from the scaled boundary finite element method; b) The geometric exact description encapsulated in the non-uniform rational B-splines basis ensures the excellent adaptability of the present approach to arbitrary free-form geometries; c) Interaction between laminated plates and elastic foundations can be easily constructed by using the proposed formulations due to discretizations are restricted only to the 2D in-plane; d) Outstanding capability of the presented formulation for the mechanical analysis of variable stiffness laminated composite plates with curvilinear fibers; e) The robust flexibility of the non-uniform rational B-splines in handling curved boundaries makes a strong adaptability of the present method to irregular meshes. Numerical examples on both static and free vibration analyses demonstrate the excellent performance of the present approach.