We develop finite element data structures for T-splines based on Bezier extraction generalizing our previous work for NURBS. As in traditional finite element analysis, the extracted Bezier elements are defined in terms of a fixed set of polynomial basis functions, the so-called Bernstein basis. The Bezier elements may be processed in the same way as in a standard finite element computer program, utilizing exactly the same data processing arrays. In fact, only the shape function subroutine needs to be modified while all other aspects of a finite element program remain the same. A byproduct of the extraction process is the element extraction operator. This operator localizes the topological and global smoothness information to the element level, and represents a canonical treatment of T-junctions, referred to as ‘hanging nodes’ in finite element analysis and a fundamental feature of T-splines. A detailed example is presented to illustrate the ideas. Copyright © 2011 John Wiley & Sons, Ltd.

Isogeometric finite element data structures based on Bézier extraction of T-splines

https://orbilu.uni.lu/bitstream/10993/14191/2/iga_final.pdf

Isogeometric analysis: an overview and computer implementation aspects

THB-splines: The truncated basis for hierarchical splines

https://apps.dtic.mil/sti/pdfs/ADA558914.pdf

An Isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces

A higher-order phase-field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework

A hierarchical approach to adaptive local refinement in isogeometric analysis

Isogeometric Analysis uses NURBS representations of the domain for performing numerical simulations. The first part of this paper presents a variational framework for generating NURBS parameterizations of swept volumes. The class of these volumes covers a number of interesting free-form shapes, such as blades of turbines and propellers, ship hulls or wings of airplanes. The second part of the paper reports the results of isogeometric analysis which were obtained with the help of the generated NURBS volume parameterizations. In particular we discuss the influence of the chosen parameterization and the incorporation of boundary conditions.

/pdf/swept-volume-parameterization-for-isogeometric-analysis-1ob4mz2w29.pdf

Anh-Vu Vuong

Papers

A hierarchical approach to adaptive local refinement in isogeometric analysis

Swept Volume Parameterization for Isogeometric Analysis

ISOGAT: A 2D tutorial MATLAB code for Isogeometric Analysis

Fundamental aspects of shape optimization in the context of isogeometric analysis

Isogeometric simulation of turbine blades for aircraft engines