Isogeometric shell analysis: The Reissner-Mindlin shell
TLDR
In this paper, a Reissner-Mindlin shell formulation based on a degenerated solid is implemented for NURBS-based isogeometric analysis and the performance of the approach is examined on a set of linear elastic and nonlinear elasto-plastic benchmark examples.About:
This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 2010-01-01 and is currently open access. It has received 621 citations till now. The article focuses on the topics: Isogeometric analysis & Shell (structure).read more
Figures
Fig. 19. Sectioned view of the buckled cylinders. ![Fig. 17. Experimental results from Kyriakides and Lee [32]](/figures/fig-17-experimental-results-from-kyriakides-and-lee-32-1cevrvrp.png)
Fig. 17. Experimental results from Kyriakides and Lee [32] 
Fig. 18. Computational results using 1440 cubic NURBS elements and 9216 Beltyschko-Tsay. Contours of plastic strain on the final configuration. 
Fig. 10. Roof loaded by velocity impulse: meshes. 
Fig. 9. Roof loaded by velocity impulse: problem description. The curved ends of the roof are hinged and the lateral boundaries are fixed. 
Fig. 1. NURBS mesh of a quarter hemisphere consisting of 6 × 6 quadratic elements. Selected corner, edge, and interior basis functions are plotted on the actual geometry, which is represented exactly.
![Fig. 17. Experimental results from Kyriakides and Lee [32]](/figures/fig-17-experimental-results-from-kyriakides-and-lee-32-1cevrvrp.webp)
Citations
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Journal ArticleDOI
Isogeometric finite element data structures based on Bézier extraction of T-splines
Michael A. Scott,Michael J. Borden,Michael J. Borden,Clemens V. Verhoosel,Thomas W. Sederberg,Thomas J. R. Hughes +5 more
TL;DR: It is shown that the extraction operator and Bézier elements provide an element structure for isogeometric analysis that can be easily incorporated into existing finite element codes, without any changes to element form and assembly algorithms, and standard data processing arrays.
Journal ArticleDOI
Isogeometric analysis: an overview and computer implementation aspects
TL;DR: An introduction to IGA applied to simple analysis problems and the related computer implementation aspects is presented, and implementation of the extended IGA which incorporates enrichment functions through the partition of unity method (PUM) is presented.
Journal ArticleDOI
The bending strip method for isogeometric analysis of Kirchhoff–Love shell structures comprised of multiple patches
TL;DR: In this article, an isogeometric formulation for rotation-free thin shell analysis of structures comprised of multiple patches is presented, where structural patches are C1- or higher-order continuous in the interior, and are joined with C0-continuity.
Journal ArticleDOI
An Isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces
Dominik Schillinger,Dominik Schillinger,Luca Dedè,Michael A. Scott,John A. Evans,Michael J. Borden,Ernst Rank,Thomas J. R. Hughes +7 more
TL;DR: It is shown that hierarchical refinement considerably increases the flexibility of this approach by adaptively resolving local features of NURBS, which combines full analysis suitability of the basis with straightforward implementation in tree data structures and simple generalization to higher dimensions.
References
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Book
The finite element method
TL;DR: In this article, the methodes are numeriques and the fonction de forme reference record created on 2005-11-18, modified on 2016-08-08.
Book
The algebraic eigenvalue problem
TL;DR: Theoretical background Perturbation theory Error analysis Solution of linear algebraic equations Hermitian matrices Reduction of a general matrix to condensed form Eigenvalues of matrices of condensed forms The LR and QR algorithms Iterative methods Bibliography.
Journal ArticleDOI
Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement
TL;DR: In this article, the concept of isogeometric analysis is proposed and the basis functions generated from NURBS (Non-Uniform Rational B-Splines) are employed to construct an exact geometric model.
Book
The NURBS Book
Les A. Piegl,Wayne Tiller +1 more
TL;DR: This chapter discusses the construction of B-spline Curves and Surfaces using Bezier Curves, as well as five Fundamental Geometric Algorithms, and their application to Curve Interpolation.