In this paper, we describe a general class of C1 smooth rational splines that enables, in particular, exact descriptions ellipses and ellipsoids — some the most important primitives for CAD CAE. The univariate are assembled by transforming multiple sets NURBS basis functions via so-called design-through-analysis compatible extraction matrices; different allowed to have polynomial degrees weight...

In this paper, we describe a general class of C1 smooth rational splines that enables, in particular, exact descriptions ellipses and ellipsoids — some the most important primitives for CAD CAE. The univariate are assembled by transforming multiple sets NURBS basis functions via so-called design-through-analysis compatible extraction matrices; different allowed to have polynomial degrees weight...

In this investigation, we successfully employed the Non-Uniform Rational B-spline (NURBS) to study fracture mechanics. NURBS functions are very popular in design field (CAD model) and it is used as an alternative Lagrange interpolation polynomials. The extended isogeometric analysis based on basis function evaluate stress intensity factors (SIFs) order control crack propagation. For various len...

Two main technologies are available to design and represent freeform surfaces: NonUniform Rational B-Splines (NURBS) and subdivision surfaces. Both representations are built on uniform B-splines, but they extend this foundation in incompatible ways, and different industries have therefore established a preference for one representation over the other. NURBS are the dominant standard for Compute...

This paper examines the role of continuity of the basis in the computation of turbulent flows. We compare standard finite elements and NURBS (non-uniform rational B-splines) discretizations that are employed in Isogeometric Analysis [23]. We make use of quadratic discretizations that are C-continuous across element boundaries in standard finite elements, and C-continuous in the case of NURBS. T...

A NURBS (non-uniform rational B-splines)-based isogeometric fluid-structure interaction formulation, coupling incompressible fluids with nonlinear elastic solids, and allowing for large structural displacements, is developed. This methodology, encompassing a very general class of applications, is applied to problems of arterial blood flow modeling and simulation. In addition, a set of procedure...

This paper presents an evolutionary structural optimisation (ESO) approach based on the boundary element method. Non-uniform rational B-splines (NURBS) are used to define the geometry of the component and, since the shape of these B-splines is governed by a set of control points, use can be made of the locations of these control points as design variables. The developed algorithm creates NURBS-...

We present a Nitche’s method to couple non-conforming two and three-dimensional NURBS (Non Uniform Rational B-splines) patches in the context of isogeometric analysis (IGA). We present results for linear elastostatics in two and and three-dimensions. The method can deal with surface-surface or volume-volume coupling, and we show how it can be used to handle heterogeneities such as inclusions. W...

This paper deals with structured grid generation using Floater’s parametrization algorithm for surface triangulation. It gives an outline of the algorithm in the context of structured grid generation. Then it explains how the algorithm can be used to generate a structured grid over a singular NURBS surface patch. This is an alternate method to the known carpeting method of reparametrization for...