NURBS-Augmented Finite Element Method for Static, Dynamic and Stability Analyses of Arbitrary Stiffened Plates

Abstract

In the present work, a new method coined as NURBS-Augmented Finite Element Method (NAFEM) has been proposed for the static, free vibration and buckling analyses of bare as well as stiffened plates of arbitrary geometries. The idea behind the present formulation originated from the concepts of Isogeometric Analysis (IGA) and NURBS-Enhanced Finite Element Method (NEFEM). In IGA, the geometry and the displacement fields are repre-sented with the NURBS basis function. As the NURBS basis functions are non-interpolating in nature they do not satisfy the Kronecker-Delta property which leads to the difficulty in enforcing the essential boundary conditions. In NEFEM, only the geometry of the elements which are at the boundaries of the plate are represented by NURBS basis function whereas the displacement function of the boundary elements are taken as piecewise polynomials. The rest of the elements which are not intersecting the boundaries are dealt with usual classical finite element techniques. Here in this present work, the NURBS basis functions are incor-porated to represent the geometry and its weakness for representing the field variables is avoided by adopting classical finite element known as ACM (Adini, Clough and Melosh) plate bending basis functions for the field variables. The efficacy of the method is shown by considering examples of various geometrical shapes and boundary conditions for all the analyses of the bare and stiffened plates.