Non-uniform rational B-splines (NURBS) have become a de facto standard in commercial modeling systems because of their power to represent both free-form shapes and some common analytic shapes. To date, however, NURBS have been viewed as purely geometric primitives, which require the designer to interactively adjust many degrees of freedom (DOFs )-control points and associated weights-to achieve...

in the present research, implementations of different computational geometry technologies in isogeometric analysis framework for computational fracture mechanics are investigated. nurbs and t-splines are two different computational geometry technologies which are studied in this work. among features of b-spline basis functions the possibility of enhancing a b-spline basis with discontinuities b...

Analysis of the laminated composite plates under transverse loading is considered using the new method of Isogeometric Analysis (IGA). Non-Uniform Rational B-Splines(NURBS)are used as shape functions for modeling the geometry of the structure and also are used as shape functions in the analysis process. To show robustness of the new technique, some examples are represented and are compared with...

The present research investigates the implementations of different computational geometry technologies in isogeometric analysis framework for computational fracture mechanics. NURBS and T-splines are two different computational geometry technologies which are studied in this work. Among the features of B-spline basis functions, the possibility of enhancing a B-spline basis with discontinuities ...

A new type of B-spline the expo-rational B-spline is introduced. The heuristic motivation for its introduction comes from important similarities in several celebrated mathematical constructions originating in approximation theory, differential geometry and operator theory. The main result of the paper is the derivation of an Edgeworth and a steepest-descent/saddlepoint asymptotic expansion whic...

An interaction integral method for evaluating mixed-mode stress intensity factors (SIFs) for two dimensional crack problems using NURBS-based isogeometric analysis method is investigated. The interaction integral method is based on the path independent J-integral. By introducing a known auxiliary field solution, the mixed-mode SIFs are calculated simultaneously. Among features of B-spline basis...

The paper develops a rational bi-cubic G2 (curvature continuous) analogue of the non-uniform polynomial C2 cubic B-spline paradigm. These rational splines can exactly reproduce parts of multiple basic shapes, such as cyclides and quadrics, in one by default smoothly-connected structure. The versatility of this new tool for processing exact geometry is illustrated by conceptual design from basic...

In this lecture we generalize the polar form and blossoming and introduce NURBS(non-uniform rational B-spline), then we extend the discussion to 2D about surfaces. 1 NURBS NURBS is an industry standard tool for the representation and design of geometry. It is the non-uniform and rational extension of B-splines. We will introduce these properties one by one using blossoming. A cubic polar form i...