Summary
This paper summarizes the development for a large displacement formulation of a membrance composed of three-node triangular elements. A formulation in terms of the deformation gradient is first constructed in terms of nodal variables. In particular, the use of the right Cauchy-Green deformation tensor is shown to lead to a particulary simple representation in terms of nodal quantities. This may then be used to construct general models for use in static and transient analyses.
Visiting Professor, CIMNE, UPC, Barcelona, Spain.
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References
Zienkiewicz OC, Taylor RL (2000) The Finite Element Method: Solid Mechanics. Volume 2. Butterworth-Heinemann, Oxford, 5th edition
Simo JC, Fox DD (1989) On a stress resultant geometrically exact shell model. Part I: Formulation and optimal parametrization. Computer Methods in Applied Mechanics and Engineering 72:267–304
Simo JC, Fox DD, Rifai MS (1989) On a stress resultant geometrically exact shell model. Part II: The linear theory; computational aspects. Computer Methods in Applied Mechanics and Engineering 73:53–92
Simo JC, Rifai MS, Fox DD (1990) On a stress resultant geometrically exact shell model. Part IV Variable thickness shells with through-the-thickness stretching. Computer Methods in Applied Mechanics and Engineering 81:91–126
Simo JC, Tarnow N (1994) A new energy and momentum conserving algorithm for the non-linear dynamics of shells. International Journal for Numerical Methods in Engineering 37:2527–2549
Büchter N, Ramm E (1992) Shell theory versus degeneration — a comparison in large rotation finite element analysis. International Journal for Numerical Methods in Engineering 34:39–59
Büchter N, Ramm E, Roehl D (1994) Three-dimensional extension of non-linear shell formulations based on the enhanced assumed strain concept. International Journal for Numerical Methods in Engineering 37:2551–2568
Braun M, Bischoff M, Ramm E (1994) Nonlinear shell formulations for complete three-dimensional constitutive laws include composites and laminates. Computational Mechanics 15:1–18
Bischoff M, Ramm E (1997) Shear deformable shell elements for large strains and rotations. International Journal for Numerical Methods in Engineering 40:4427–49
Bischoff M, Ramm E (1999) Solid-like shell or shell-like solid formulation? A personal view. In W. Wunderlich, editor, Proc. Eur Conf on Comp. Mech (ECCM’99 on CD-ROM), Munich, September
Ramm E (1999) From Reissner plate theory to three dimensions in large deformation shell analysis. Z. Angew. Math. Mech. 79:1–8
Bischoff M, Ramm E (2000) On the physical significance of higher order kinematic and static variables in a three-dimensional shell formulation. International Journal of Solids and Structures 37:6933–60
Bletzinger K-U, Bischoff M, Ramm E (2000) A unified approach for shearlocking-free triangular and rectangular shell finite elements. Computers and Structures 75:321–34
Schweizerhof K, Ramm E (1984) Displacement dependent pressure loads in non-linear finite element analysis. Computers and Structures 18(6):1099–1114
Simo JC, Taylor RL, Wriggers P (1991) A note on finite element implementation of pressure boundary loading. Communications in Applied Numerical Methods 7:513–525
Newmark N (1959) A method of computation for structural dynamics. Journal of the Engineering Mechanics Division 85:67–94.
Zienkiewicz OC, Taylor RL (2000) The Finite Element Method: The Basis. Volume 1, Butterworth-Heinemann, Oxford, 5th edition
Taylor RL FEAP-A Finite Element Analysis Program, Programmer Manual. University of California, Berkeley, http://www.ce.berkeley.edu/~rlt
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Taylor, R.L., Oñate, E., Ubach, PA. (2005). Finite Element Analysis of Membrane Structures. In: Oñate, E., Kröplin, B. (eds) Textile Composites and Inflatable Structures. Computational Methods in Applied Sciences, vol 3. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3317-6_4
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DOI: https://doi.org/10.1007/1-4020-3317-6_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-3316-2
Online ISBN: 978-1-4020-3317-9
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