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Computational Science, Engineering & Technology Series
ISSN 1759-3158
Edited by: B.H.V. Topping, Z. Bittnar
Chapter 2

Nonlinear Shell Problem Formulation accounting for Through-the-Thickness Stretching and its Finite Element Implementation

A. Ibrahimbegovic+, B. Brank* and J. Korelc*

+Ecole Normale Superieure de Cachan, France
*Faculty of Civil and Geodetic Engineering, University of Ljubljana, Slovenia

Full Bibliographic Reference for this chapter
A. Ibrahimbegovic, B. Brank, J. Korelc, "Nonlinear Shell Problem Formulation accounting for Through-the-Thickness Stretching and its Finite Element Implementation", in B.H.V. Topping, Z. Bittnar, (Editors), "Computational Structures Technology", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 2, pp 33-62, 2002. doi:10.4203/csets.7.2
Keywords: nonlinear shells, thickness change, incompatible modes.

In this work we discuss the theoretical formulation of a shell model accounting for the through-the-thickness stretching, which provides a very important advantage to allow for large deformations and direct application of 3d constitutive equations. Three different possibilities for parameterizing the proposed shell model are examined in view of the subsequent finite element implementation, with the first choice leading to 7 nodal parameters and the remaining two to 6 nodal parameters. Comparisons are performed of the 7-parameter shell model with no simplification of kinematics terms and 7-parameter shell model which exploits usual simplifications of Green-Lagrange strain measures where only terms with linear variation in through-the-thickness direction is retained. Further comparisons are presented between two different possibilities of implementing the incompatible mode method for reducing the number of shell model parameters to 6. One implementation uses an additive decomposition of the Green-Lagrange strains and the other one employs an additive decomposition of the displacement gradient leading to the multiplicative decomposition of deformation gradient. Several numerical examples are given to illustrate performance of the shell elements developed herein.

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