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Shell Element Formulations for General Nonlinear Analysis. Modeling Techniques

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

Part of the book series: SpringerBriefs in Applied Sciences and Technology ((BRIEFSCOMPUTAT))

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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Notes

  1. 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. 2.

    Some authors use the notation \( {}^{o}\underline{g}^{i} \otimes {}^{o}\underline{g}^{j} \).

  3. 3.

    Please notice that shell elements are not compatible with Bernoulli beam elements.

References

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Authors and Affiliations

  1. SIM&TEC, Av. Pueyrredón 2130, Buenos Aires, Argentina

    Eduardo N. Dvorkin & Rita G. Toscano

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  1. Eduardo N. Dvorkin
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  2. Rita G. Toscano
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Correspondence to Eduardo N. Dvorkin .

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Dvorkin, E.N., Toscano, R.G. (2013). Shell Element Formulations for General Nonlinear Analysis. Modeling Techniques. In: Finite Element Analysis of the Collapse and Post-Collapse Behavior of Steel Pipes: Applications to the Oil Industry. SpringerBriefs in Applied Sciences and Technology(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37361-9_2

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

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