Non-uniform rational B-splines (NURBS) are a convenient way to integrate CAD software and analysis codes, saving time from the operator allowing efficient solution schemes that can be employed in of complex mechanical problems. In this paper, Isogeometric Boundary Element Method coupled with Bézier extraction NURBS conventional BEM used for 2D contact problems under cyclic loads. A node-pair ap...

The isogeometric analysis is increasingly used in various engineering problems. It is based on Non-Uniform Rational B-Splines (NURBS) basis function applied for the solution field approximation and the geometry description. One of the major concerns with this method is finding an efficient approach to impose essential boundary conditions, especially for inhomogeneous boundaries. The main contri...

GeoPDEs (http://geopdes.sourceforge.net) is a suite of free software tools for applications on Isogeometric Analysis (IGA). Its main focus is on providing a common framework for the implementation of the many IGA methods for the discretization of partial differential equations currently studied, mainly based on B-Splines and Non-Uniform Rational B-Splines (NURBS), while being flexible enough to...

Merging NURBS surfaces together and extending existing ones are common problems in CAD systems. Extending existing surface is usually done by creating a new separate surface and applying some merging function – result is one continuous surface. In this paper, full description of a method of direct extending existing surfaces is introduced. The extension of the surface is recomputed during its c...

Symbolic computation of NURBS plays an important role in many areas of NURBSbased geometric computation and design. However, any nontrivial symbolic computation, especially when rational B-splines are involved, would typically result in B-splines with high degrees. In this paper we develop degree reduction strategies for NURBS symbolic computation on curves. The specific topics we consider incl...

Constructing a CAD model from a physical model plays a key role in some productdevelopment processes. To be presented is an “indirect” method of fitting NURBS-surfaces for rotational-freeform shapes: 1) Cloud-of-points data representing a rotational-freeform shape are transformed into an orthogonal-coordinate (sphericalor cylindrical-) system, 2) a single-valued Bspline surface is fitted to the...

Non-Uniform Rational B-Spline (NURBS) surfaces are commonly used within Computer-Aided Design (CAD) tools to represent geometric objects. When using isogeometric analysis (IGA), it is possible use such NURBS geometries for numerical directly. Analyzing fluid flows, however, requires complex three-dimensional flow domains. Defining a parametrization of volumetric domains can be challenging and s...

Isogeometric analysis (IGA) is an effective numerical method for connecting computer-aided design and engineering, which has been widely applied in various aspects of computational mechanics. IGA involves Galerkin collocation formulations. Exploiting the same high-order non-uniform rational B-spline (NURBS) bases that span physical domain solution space leads to increased accuracy fast computat...

We present a parallel GPU-accelerated algorithm for computing the directed Hausdorff distance from one NURBS surface to another, within a bound. We make use of axis-aligned bounding-box hierarchies that bound the NURBS surfaces to accelerate the computations. We dynamically construct as well as traverse the bounding-box hierarchies for the NURBS surfaces using operations that are optimized for ...