Article history: Received 11 April 2013 Received in revised form 16 December 2013 Accepted 5 January 2014 Available online 13 January 2014

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...

One primary problem in shape optimization of structures is making a robust link between design model (geometric description) and analysis model. This paper investigates the potential of Isogeometric Analysis (IGA) for solving this problem. The generic framework of shape optimization of structures is presented based on Isogeometric analysis. By discretization of domain via NURBS functions, the a...

Micro Abstract We present a framework for isogeometric analysis on unstructured quadrilateral meshes. Acknowledging the differing requirements posed by design and analysis, we propose the construction of a separate, smooth spline space for each, while ensuring isogeometric compatibility. A key ingredient in the approach is the use of singular parameterizations at extraordinary vertices. We demo...

This paper outlines and qualitatively compares the implementations of seven different methods for solving Poisson’s equation on the disk. The methods include two classical finite elements, a cotan formula-based discrete differential geometry approach and four isogeometric constructions. The comparison reveals numerical convergence rates and, particularly for isogeometric constructions based on ...

We begin the mathematical study of Isogeometric Analysis based on NURBS (non-uniform rational B-splines.) Isogeometric Analysis is a generalization of classical Finite Element Analysis (FEA) which possesses improved properties. For example, NURBS are capable of more precise geometric representation of complex objects and, in particular, can exactly represent many commonly engineered shapes, suc...

Article history: Available online 20 March 2015

Isogeometric analysis (IGA) has been recently introduced as a viable alternative to the standard, polynomial-based finite element analysis. One of the fundamental performance issues of the isogeometric analysis is the quadrature of individual components of the discretized governing differential equation. The capability of the isogeometric analysis to easily adopt basis functions of high degree ...

We propose Floating Isogeometric Analysis (FLIGA), which extends IGA to extreme deformation analysis. The method is based on a novel tensor-product construction of B-Splines for the update basis functions in one direction parametric space. With “floating” deformation-dependently this direction, mesh distortion overcome problems deformations occur predominantly along associated (possibly curved)...