Modélisation du plissage dans les structures membranaires
Keywords:
finite element, membranes, hyperelasticity, bifurcation, wrinklesAbstract
The problem of the wrinkling of the membranes is addressed in this paper within the total Lagrangian formulation. The material obeys a compressible hyperelastic constitutive equation and the resulting finite elements are either 8-node quadrilateral or 6- node triangular membrane elements without flexural stiffness. The appearance of wrinkles in the membrane structures is dealt with using the bifurcation analysis without any imperfections. The standard spherical arclength method is modified by means of a specific solution procedure to cope with the occurrence of complex roots when solving the quadratic constraint equation. Applying the proposed formulation to a set of typical numerical examples shows its ability to correctly predict the wrinkling behaviour in membranes structures.
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References
Adler A.L., Finite element approaches for static and dynamic analysis of partially wrinkled
membrane structures, PhD Thesis, Departement of Aerospace Engineering, University of
Colorado, Boulder, CO, USA, 2000.
Bergan P.G., Horrigmoe G., Krakeland B., Soreide B., « Solution techniques for non-linear
finite element problems », International Journal for Numerical Methods in Engineering,
vol. 12, 1978, p. 1677-1696.
Cirak F., Ortiz M., « Fully C1-conforming subdivision elements for finite deformations thinshell
analysis », International Journal for Numerical Methods in Engineering, vol. 51,
, p. 813-833.
Contri P., Schrefler B.A., « A geometrically nonlinear finite element analysis of wrinkled
membrane surface by no-compression material model », Communication in Applied
Numerical Methods, vol. 4, 1988, p. 5-15.
Crisfield M.A., Non-linear Finite Element Analysis of Solids and Structures, Volume 1, John
Wiley & Sons, 1991.
Flores F.G., Onate E., « Rotation-free element for finite strain analysis of elastic-plastic thin
shell and membrane structure », Textile composites and inflatable structures, Onate E and
Kröplin B (Eds.), CIMNE: Barcelona, 2003, p. 148-153.
Fujikake M., Kojima O., Fukushima S., « Analysis of fabric tension structures », Computers
& Structures, vol. 32, 1989, p. 537-547.
Kang S., Im S., « Finite element analysis of wrinkling membranes », Journal of Applied
Mechanics, vol. 64, 1997, p. 263-269.
Lam W.F., Morley C.T., « Arc-length method for passing limit points in structural
calculation », Journal of Structural Engineering, vol. 118, 1992, p. 19-185.
Miller R.K., Hedgepeth J.M., « An algorithm for finite element analysis of partly wrinkled
membranes », AIAA, vol. 20, 1982, p. 1761Β1763.
Miller R.K., Hedgepeth J.M., Weingarten V.I., Das P., Kahyai S., « Finite element analysis of
partly wrinkled membranes », Computers & Structures, vol. 20, 1985, p. 631Β639.
Miyamura T., « Wrinkling on stretched circular membrane under in-plane torsion:
birfurcation analyses and experiments », Engineering Structures, vol. 23, 2000, p. 1407-
Riks E., « The application of Newton’s method to the problem of elastic stability », Journal of
Applied Mechanics, vol. 39, 1972, p. 1060-1066.
Riks E., « An incremental approach to the solution of snapping and buckling problems »,
International Journal of Solids and Structures, vol. 15, 1979, p. 529-551.
Shi J., Moita G.F., « The post-critical analysis of axisymmetric hyper-elastic membranes by
the finite element method », Computer Methods in Applied Mechanics and Engineering,
vol. 135, 1996, p. 265-281.
Stanuszek M., « FE analysis of large deformations of membranes with wrinkling », Finite
Elements in Analysis and Design, vol. 39, 2003, p. 599-618.
Szyszkowski W., Glockner G., « Spherical membranes subjected to vertical concentrated
loads: an experimental study », International Journal of Engineering Structures, vol. 9,
, p. 183-192.
Tabarrok B., Qin Z., « Nonlinear analysis of tension structures », Computers & Structures,
vol. 45, 1992, p. 973Β984.
Tessler A., Sleight D.W., Wang JT., « Nonlinear shell modelling of thin membranes with
emphasis on structural wrinkling », 44th AIAA/ASME/ASCE/AHS Structures, Structural
dynamics, and Materials Conference, Nortfolk, Virginia, USA, AIAA 2003-1931.
Wagner W., Wriggers P., « A simple method for the calculation of post-critical branches »,
Engineering and Computations, vol. 5, 1988, p. 103-109.
Wempner GA., « Discrete approximations related to nonlinear theories of solids »,
International Journal of Solids and Structures, vol. 7, 1971, p. 1581-1599.
Wong Y.W., Pellegrino S., « Amplitude of wrinkles in thin membranes », In New approaches
to structural mechanics shells and biological structures, (Dordrecht, The Netherlands,
a), Kluwer Academic Publishers, 257-270.
Wong Y.W., Pellegrino S., « Computation of wrinkle amplitudes in thin membranes »,
rd AIAA Structures, Structural dynamics, and Materials Conference, Denver, Co, USA,
AIAA-2002b-1369.
