3d-Shell Elements and Their Underlying Mathematical Model

Chapelle, Dominique; Ferent, Anca; Bathe, Klaus‐Jürgen

doi:10.1142/s0218202504003179

Cited by 33 publications

(54 citation statements)

References 22 publications

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“…We use a coarse mesh, made of 4800 tetraedra (3916 degrees of freedom) for the fluid, and 40 hexaedra (1584 degrees of freedom) for the structure. We set ∆t = 10 −4 s. The structure is modeled by 3D-shell elements (see [4][5][6]) with a Saint Venant-Kirchhoff constitutive law and the physical parameters E = 3 · 10 6 dynes/cm 2 , ν = 0.3 and ρ s = 1.2g/cm 3 . The thickness of the shell is h = 0.1cm.…”

Section: Preliminary Numerical Resultsmentioning

confidence: 99%

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Domain decomposition based Newton methods for fluid-structure interaction problems

et al. 2008

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Abstract. We review various fluid-structure algorithms based on domain decomposition techniques and we propose a new one. The standard methods used in fluid-structure interaction problems are generally "nonlinear on subdomains". We propose a scheme based on the principle "linearize first, then decompose". In other words we extend to fluid-structure problems domain decomposition techniques classically used in nonlinear elasticity.Résumé. Nous faisons une revue de divers algorithmes de couplage fluide-structure basés sur des techniques de décomposition de domaine et nous en proposons une nouvelle. Les méthodes classiquement utilisées en interaction fluide-structure sont généralement "non linéaires par sous-domaine". Le schéma que nous proposons est au contraire basé sur le principe "linéariser puis décomposer". Autrement dit, nousétendons aux problèmes d'interaction fluide-structure des techniques de décomposition de domaine classiquement utilisées enélasticité non linéaire.

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Section: Preliminary Numerical Resultsmentioning

confidence: 99%

“…To model the structure, we use 3D-shell elements, which allows us to use three dimensional consititutive laws (see [4][5][6]). Up to our knowledge, this is the first time such elements are used in fluid-structure interaction.…”

Section: Introductionmentioning

confidence: 99%

Domain decomposition based Newton methods for fluid-structure interaction problems

et al. 2008

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“…(1) [3,8]. Hence, in our discussion of finite element convergence issues we can use the generic formulation (1) to focus on the underlying difficulties to properly measure convergence of finite element procedures.…”

Section: The Governing Shell Equationsmentioning

confidence: 99%

Measuring the convergence behavior of shell analysis schemes

Bathe

Lee

2011

Computers & Structures

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a b s t r a c tWhile shells have been analyzed abundantly for many years in engineering and the sciences, improved finite element and related analysis methods are still much desired and researched. More general and effective finite element procedures are needed for complex shell structures, including for the analysis of composite shells and the optimization of shells. In this paper we discuss how finite element methods, and other analysis techniques, should be tested in order to identify their reliability and effectiveness. We summarize some important theoretical results, present appropriate test problems and convergence measures, and we illustrate our discussion through some novel numerical results. An important conclusion is that the testing has to be performed very carefully in order to obtain relevant results, and we show how this is accomplished in detail.

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“…Of course, we are still continuing our research to improve these shell elements [ 111. We also work to improve, as well, the effectiveness of triangular elements [12] and to include three-dimensional through-the-thickness effects [13]. In metal forming, it can be important to include the through-the-kckness stress and strain effects, and shell elements with quadratic displacement interpolations through the thickness are then effective 1131.…”

Section: Mathematical Conditions On Finite Elementsmentioning

confidence: 99%

On the State of Finite Element Procedures for Forming Processes

Bathe¹

2004

AIP Conference Proceedings

149

154

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Abstract. The solution of forming processes requires reliable and efficient finite element methods to model the various complex physical phenomena encountered. The objective in this presentation is to focus on the current state of finite element methods with respect to reliability and efficiency in modeling forming processes. The finite element procedures pertain to the simulation of sheet metal forming, bulk forming, extrusion and drawing, rolling, welding, cutting processes, etc. It is emphasized that the appropriate finite element methods for a specific problem should be used, and that indeed procedures are available which are effective in many situations. The presentation briefly considers the state of modeling of solids, shell structures, contact conditions, friction, inelastic material response in large strains, thermomechanical coupling and fluid-solid interactions, as encountered in forming process simulations. The solutions of the governing finite element models are obtained using sparse direct or iterative solvers. The oral presentation will include the results of various example simulations.

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3d-Shell Elements and Their Underlying Mathematical Model

Cited by 33 publications

References 22 publications

Domain decomposition based Newton methods for fluid-structure interaction problems

Domain decomposition based Newton methods for fluid-structure interaction problems

Measuring the convergence behavior of shell analysis schemes

On the State of Finite Element Procedures for Forming Processes

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