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2013 | OriginalPaper | Chapter

2. Shell Element Formulations for General Nonlinear Analysis. Modeling Techniques

Authors : Eduardo N. Dvorkin, Rita G. Toscano

Published in: Finite Element Analysis of the Collapse and Post-Collapse Behavior of Steel Pipes: Applications to the Oil Industry

Publisher: Springer Berlin Heidelberg

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Abstract

In 1970, Ahmad et al. [1] presented a shell element formulation that after many years still constitutes the basis for modern finite element analysis of shell structures. The original formulation was afterwards extended to material and geometric nonlinear analysis under the constraint of the infinitesimal strains assumption [2–4].

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previous chapter Introduction
next chapter Collapse and Post-Collapse Behavior of Steel Pipes. Finite Element Models
Footnotes
1
We use Einstein’s notation: \( a_{k} b_{k} \equiv \sum\nolimits_{k} {a_{k} } b_{k} \), that is to say repeated indices indicate a summation.
 
2
Some authors use the notation \( {}^{o}\underline{g}^{i} \otimes {}^{o}\underline{g}^{j} \).
 
3
Please notice that shell elements are not compatible with Bernoulli beam elements.
 
Literature
1.
Ahmad S, Irons B, Zienkiewicz O (1970) Analysis of thick and thin shell structures by curved finite elements. Int J Numer Methods Eng 2:419–451CrossRef
2.
Ramm E (1977) A plate/shell element for large deflections and rotations. In: Bathe et al (ed) Formulations and computational algorithms in finite element analysis. MIT Press, Cambridge
3.
Kråkeland B (1978) Nonlinear analysis of shells using degenerate isoparametric elements. In: Bergan et al (ed), Finite elements in nonlinear mechanics. Tapir Publishers, Norwegian Institute of Technology, Trondheim
4.
Bathe K-J, Bolourchi S (1980) A geometric and material nonlinear plate and shell element. Comput Struct 11:23–48MATHCrossRef
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Bathe K-J (1996) Finite element procedures. Prentice Hall, Saddle River
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Zienkiewicz O, Taylor R (2000) The finite element method. Butterworth-Heinemann, OxfordMATH
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Dvorkin EN, Bathe K-J (1984) A continuum mechanics based four-node shell element for general nonlinear analysis. Eng Comput 1:77–88CrossRef
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Bathe K-J, Dvorkin EN (1985) A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation. Int J Numer Methods Eng 21:367–383MATHCrossRef
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Bathe K-J, Dvorkin EN (1986) A formulation of general shell elements—the use of mixed interpolation of tensorial components. Int J Numer Methods Eng 22:697–722MATHCrossRef
10.
Rodal J, Witmer E (1979) Finite-strain large-deflection elastic-viscoplastic finite-element transient analysis of structure. NASA CR 159874
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Hughes T, Carnoy E (1983) Nonlinear finite element shell formulation accounting for large membrane strains. Comput Methods Appl Mech Eng 39:69–82MATHCrossRef
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Simo J, Fox D (1989) On a stress resultant geometrically exact shell model. Part I: Formulation and optimal parametrization. Comput Methods Appl Mech Eng 72:267–304MathSciNetMATHCrossRef
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Simo J, Fox D, Rifai M (1989) On a stress resultant geometrically exact shell model. Part II: The linear theory; computational aspects. Comput Methods Appl Mech Eng 72:53–92MathSciNetCrossRef
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Simo J, Fox D, Rifai M (1990) On a stress resultant geometrically exact shell model. Part III: Computational aspects of the nonlinear theory. Comput Methods Appl Mechs Eng 79:21–70MathSciNetMATHCrossRef
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Simo J, Fox D, Rifai M (1992) On a stress resultant geometrically exact shell model. Part IV: Variable thickness shells with through-the-thickness stretching. Comput Methods Appl Mech Eng 81:91–126MathSciNetCrossRef
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Simo J, Kennedy J (1992) On a stress resultant geometrically exact shell model. Part V: Nonlinear plasticity formulation and integration algorithms. Comput Methods Appl Mech Eng 96:133–171MathSciNetMATHCrossRef
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Büchter M, Ramm E, Roehl D (1994) Three-dimensional extension of non-linear shell formulation based on the enhanced assumed strain concept. Int J Numer Methods Eng 37:2551–2568MATHCrossRef
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Bischoff M, Ramm E (1997) Shear deformable shell elements for large strains and rotations. Int J Numer Methods Eng 40:4427–4449MATHCrossRef
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Dvorkin EN, Pantuso D, Repetto E (1995) A formulation of the MITC4 shell element for finite strain elasto-plastic analysis. Comput Methods Appl Mech Eng 125:17–40CrossRef
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21.
Toscano RG, Dvorkin EN (2007) A shell element for finite strain analyses. Hyperelastic material models. Eng Comput 24:514–535MATHCrossRef
22.
Toscano RG, Dvorkin EN (2008) A new shell element for elasto-plastic finite strain analyzes. Application to the collapse and post-collapse analysis of marine pipelines. In: Abel J, Cooke J (eds), Proceedings 6th international conference on computation of shell & spatial structures, Spanning Nano to Mega. Ithaca
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Dvorkin EN, Oñate E, Oliver X (1988) On a nonlinear formulation for curved Timoshenko beam elements considering large displacement/rotation increments. Int J Numer Methods Eng 26:1597–1613MATHCrossRef
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Dvorkin EN, Goldschmit MB (2005) Nonlinear continua. Springer, Berlin
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Dvorkin EN (1992) On nonlinear analysis of shells using finite elements based on mixed interpolation of tensorial components. In: Rammerstorfer F (ed) Nonlinear analysis of shells by finite elements. Springer, New York
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Gebhardt H, Schweizerhof K (1993) Interpolation of curved shell geometries by low order finite elements—errors and modifications. Int J Numer Methods Eng 36:287–302MATHCrossRef
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Simo J, Hughes T (1998) Computational inelasticity. Springer, New YorkMATH
Metadata
Title
Shell Element Formulations for General Nonlinear Analysis. Modeling Techniques
Authors
Eduardo N. Dvorkin
Rita G. Toscano
Copyright Year
2013
Publisher
Springer Berlin Heidelberg
Book
Finite Element Analysis of the Collapse and Post-Collapse Behavior of Steel Pipes: Applications to the Oil Industry

Print ISBN: 978-3-642-37360-2

Electronic ISBN: 978-3-642-37361-9

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-3-642-37361-9_2

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