Summary
This paper shows applications of a recently developed shell element to the analysis of thin shell and membrane structures. The element is a three node triangle with only translational DOFs (rotation free) that uses the configuration of the three adjacent elements to evaluate the strains. This allows to compute (constant) bending strains and (linear) membrane strains. A total Lagrangian formulation is used. Strains are defined in terms of the principal stretches. This allows to consider rubber materials and other type of materials using the Hencky stress-strain pair. An explicit central difference scheme is used to integrate the momentum equations. Several examples, including inflation and deflation of membranes show the excellent convergence properties and robustness of the element for large strain analysis of thin shells and membranes.
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References
Taylor RL (2001) Finite element analysis of membrane structures. Publication 203, CIMNE, Barcelona
Oñate E (1994) A review of some finite element families for thick and thin plate and shell analysis. Publication 53, CIMNE, Barcelona
Hampshire JK, Topping BHV, Chan HC (1992) Three node triangular elements with one degree of freedom per node. Engng Comput 9:49–62
Phaal R, Calladine CR (1992) A simple class of finite elements for plate and shell problems. II: An element for thin shells with only translational degrees of freedom. Num Meth Engng 35:979–996
Oñate E, Cervera M. (1993) Derivation of thin plate bending elements with one degree of freedom per node. Engineering Computations 10:553–561
Oñate E, Zárate F (2000) Rotation-free plate and shell triangles. Num Meth Engng 47:557–603
Cirak F, Ortiz M (2000) Subdivision surfaces: A new paradigm for thin-shell finite element analysis. Num Meths Engng 47:2039–2072
Flores FG, Oñate E (2001) A basic thin shell triangle with only translational DOFs for large strain plasticity. Num Meths Engng 51:57–83
Cirak F, Ortiz M (2001) Fully C1-conforming subdivision elements for finite deformations thin-shell analysis. Num Meths Engng 51:813–833
Flores FG, Oñate E. (2003) Improvements in the membrane behaviour of the three node rotation-free BST shell triangle using an assumed strain approach. Comput Meth Appl Mech Engng (in press)
Zienkiewicz OC, Taylor RL (2000) The finite element method. Vol II: Solid Mechanics, Butterworth-Heinemann, place?
Oñate E, Flores FG (2004) Advances in the formulation of the rotation-free basic shell. Comput Meth Appl Mech Engng (in press)
Ogden RW (1972) Large deformation isotropic elasticity: on the correlation of theory and experiments for incompressible rubberlike solids. Proc Royal Society London A326:565–584
Cook RD (1974) Improved two-dimensional finite element, ASCE J Struct Div 100(ST6):1851–1863
Huang HC (1989) Static and Dynamic Analysis of Plates and Shells. Springer-Verlag, Berlin
Needleman A (1977) Inflation of spherical rubber ballons. Solids and Structures 13:409–421
STAMPACK (2003) A General Finite Element System for Sheet Stamping and Forming Problems, Quantech ATZ, Barcelona
Marklund PO. Nilsson L (2002) Simulation of airbag inflation processes using a coupled fluid structure approach. Computational Mechanics 29:289–297
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Flores, F.G., Oñate, E. (2005). Applications of a Rotation-Free Triangular Element for Finite Strain Analysis of Thin Shells and Membranes. 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_5
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DOI: https://doi.org/10.1007/1-4020-3317-6_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-3316-2
Online ISBN: 978-1-4020-3317-9
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