Free Flexural Vibration Analysis of Thin Plates Using NURBS-Augmented Finite-Element Method

In isogeometric analysis (IGA), the non-uniform rational B-spline (NURBS) basis functions are used for depicting the geometry and the displacement field. As the NURBS basis functions are non-interpolating in nature, the enforcement of essential boundary condition becomes a difficult task. In order to circumvent the above problem, recently the authors Mishra and Barik (Comput 232:105869, 2020; Eng Comput 35:351-362, 2019) proposed a new method called NURBS-augmented finite-element method (NAFEM). The authors have incorporated the non-uniform rational B-spline (NURBS) basis functions for the representation of the geometry and the usual finite-element basis functions are adopted for the field variables as they satisfy the Kronecker-Delta property. This simplifies the implementation of the boundary condition to a great extent. In the present work, NAFEM is extended for free vibration analysis of plates having different geometries and boundary conditions, and the results are found to be in excellent agreement with the existing ones. To showcase the robustness of NAFEM, some arbitrary-shaped plates have also been considered, and the new results are presented.