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Journal ArticleDOI

Isogeometric fluid-structure interaction: theory, algorithms, and computations

TL;DR: A fully-coupled monolithic formulation of the fluid-structure interaction of an incompressible fluid on a moving domain with a nonlinear hyperelastic solid is presented.
Abstract: We present a fully-coupled monolithic formulation of the fluid-structure interaction of an incompressible fluid on a moving domain with a nonlinear hyperelastic solid. The arbitrary Lagrangian–Eulerian description is utilized for the fluid subdomain and the Lagrangian description is utilized for the solid subdomain. Particular attention is paid to the derivation of various forms of the conservation equations; the conservation properties of the semi-discrete and fully discretized systems; a unified presentation of the generalized-α time integration method for fluid-structure interaction; and the derivation of the tangent matrix, including the calculation of shape derivatives. A NURBS-based isogeometric analysis methodology is used for the spatial discretization and three numerical examples are presented which demonstrate the good behavior of the methodology.
Citations
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Journal ArticleDOI
TL;DR: T-splines, a generalization of NURBS enabling local refinement, have been explored as a basis for isogeometric analysis in this paper, and they have shown good results on some elementary two-dimensional and three-dimensional fluid and structural analysis problems and attain good results in all cases.

975 citations

Journal ArticleDOI
TL;DR: 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.

621 citations

Journal ArticleDOI
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.
Abstract: 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.

566 citations


Cites methods from "Isogeometric fluid-structure intera..."

  • ...Investigations using simple tensor product NURBS constructions have shown that the use of a smooth basis in analysis provides computational advantages over standard finite elements in many areas including turbulence [3, 4, 5], fluid-structure interaction [6, 7, 8], incompressibility [9, 10, 11], structural...

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Journal ArticleDOI
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.

522 citations


Cites methods from "Isogeometric fluid-structure intera..."

  • ...We also review some of the recent attempts at simplifying the CAD-FEA integration by separating boundary and domain discretisations....

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References
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Journal ArticleDOI
TL;DR: An iterative method for solving linear systems, which has the property of minimizing at every step the norm of the residual vector over a Krylov subspace.
Abstract: We present an iterative method for solving linear systems, which has the property of minimizing at every step the norm of the residual vector over a Krylov subspace. The algorithm is derived from t...

10,907 citations


"Isogeometric fluid-structure intera..." refers methods in this paper

  • ...Solve this linear system using a preconditioned GMRES algor ithm (see Saad and Schultz [52]) to a specified tolerance....

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  • ...(1) Evaluate iterates at the intermediate time levels as Un+αf ,(l) = Un + αf(Un+1,(l−1) − Un) (184) U̇n+αf ,(l) = U̇n + αf(U̇n+1,(l−1) − U̇n) (185) Ün+αm,(l) = Ün + αm(Ün+1,(l−1) − Ün) (186) V n+αf ,(l) = V n + αf(V n+1,(l−1) − V n) (187) V̇ n+αf ,(l) = V̇ n + αf(V̇ n+1,(l−1) − V̇ n) (188) V̈ n+αm,(l) = V̈ n + αm(V̈ n+1,(l−1) − V̈ n) (189) P n+1,(l) = P n+1,(l−1) (190) (2) Use the intermediate solutions to assemble the residualof the continuity and momentum equations and the corresponding matrices in the linear system ∂Rmom ∂Ün+1 ∆Ün+1,(l) + ∂Rmom ∂P n+1 ∆P n+1,(l) + ∂Rmom ∂V̈ n+1 ∆V̈ n+1,(l) = −R mom (l) (191) ∂Rcon ∂Ün+1 ∆Ün+1,(l) + ∂Rcon ∂P n+1 ∆P n+1,(l) + ∂Rcon ∂V̈ n+1 ∆V̈ n+1,(l) = −R con (l) (192) ∂Rmesh ∂Ün+1 ∆Ün+1,(l) + ∂Rmesh ∂P n+1 ∆P n+1,(l) + ∂Rmesh ∂V̈ n+1 ∆V̈ n+1,(l) = −R mesh (l) (193) (194) Solve this linear system using a preconditioned GMRES algorithm (see Saad and Schultz [52]) to a specified tolerance....

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Journal ArticleDOI
TL;DR: In this article, a new finite element formulation for convection dominated flows is developed, based on the streamline upwind concept, which provides an accurate multidimensional generalization of optimal one-dimensional upwind schemes.

5,157 citations


"Isogeometric fluid-structure intera..." refers methods in this paper

  • ...The residual-based formulation of fluid flow may be viewed as an extension of well-known stabilized methods, such as SUPG [ 10 ]....

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Journal ArticleDOI
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.

5,137 citations

Book
23 Nov 2011
TL;DR: Variational Formulations and Finite Element Methods for Elliptic Problems, Incompressible Materials and Flow Problems, and Other Applications.
Abstract: Variational Formulations and Finite Element Methods. Approximation of Saddle Point Problems. Function Spaces and Finite Element Approximations. Various Examples. Complements on Mixed Methods for Elliptic Problems. Incompressible Materials and Flow Problems. Other Applications.

5,030 citations