A geometrically exact thin membrane model - Investigation of large deformations and wrinkling

International Journal for Numerical Methods in Engineering

Volumn 74, Issue 6, 2008, Pages 871-893

  Weinberg, Kerstin ^a   Neff, Patrizio ^b  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^b DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Buckling; Energy minimization; Membranes; Shells; Tension field theory; Thin films; Transverse shear; Viscoelasticity; Wrinkling

Indexed keywords

BUCKLING; DEFORMATION; LINEARIZATION; MATHEMATICAL MODELS; MEMBRANES; ROTATION; VISCOELASTICITY; VISCOSITY;

TENSION-FIELD THEORY; TRANSVERSE SHEAR; WRINKLING;

SHELLS (STRUCTURES);

BUCKLING; DEFORMATION; LINEARIZATION; MATHEMATICAL MODELS; MEMBRANES; ROTATION; SHELLS (STRUCTURES); VISCOELASTICITY; VISCOSITY;

EID: 43349093493     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2189     Document Type: Article

References (26)

1. Ramm E, Wall WA. Shell structures - a sensitive interrelation between physics and numerics. International Journal for Numerical Methods in Engineering 2004; 60:381-427.
2. Ciarlet PG. Introduction to Linear Shell Theory (1st edn). Series in Applied Mathematics. Gauthier-Villars: Paris, 1998.
3. Ortiz M, Gioia G. The morphology and folding patterns of buckling-driven thin-film blisters. Journal of the Mechanics and Physics of Solids 1994; 42:531-559.
4. Jenkins CHM. Gossamer Spacecraft: Membranes and Inflatable Structures Technology for Space Applications. American Institute of Aeronautics and Astronautics: New York, 2001.
5. Steigmann DJ. Tension-field theory. Proceedings of the Royal Society of London, Series A 1990; 429:141-173.
6. Wagner H. Ebene Blechwandträger mit dünnem Stegblech. Zeitschrift für Flugtechnik und Motorluftschiffahrt 1929; 20:8-12.
7. Reissner E. On tension field theory. Proceedings of the 5th International Congress on Applied Mechanics, vol. 5, 1938; 88-92.
8. Pipkin AC. Relaxed energy densities for large deformations of membranes. IMA Journal of Applied Mathematics 1994; 52:297-308.
9. Le Dret H, Raoult A. The membrane shell model in nonlinear elasticity: a variational asymptotic derivation. Journal of Nonlinear Science 1996; 6:59-84.
10. Roddeman D. The wrinkling of thin membranes: part I-theory. Journal of Applied Mechanics 1987; 54:884-887.
11. Roddeman D. Finite element analysis of wrinkling membranes. Communications in Applied Numerical Methods 1991; 7:299-307.
12. Neff P. A geometrically exact viscoplastic membrane-shell with viscoelastic transverse shear resistance avoiding degeneracy in the thin-shell limit. Part I: The viscoelastic membrane-plate. Zeitschrift Angewandre Mathematik Physik 2005; 56(1):148-182. DOI: 10.1007/s00033-004-4065-0(Preprint 2337, http://wwwbib.mathematik.tudarmstadt.de/Math-Net/Preprints/Listen/ pp04.html).
13. Neff P. Finite multiplicative plasticity for small elastic strains with linear balance equations and grain boundary relaxation. Continuum Mechanics and Thermodynamics 2003; 15(2):161-195.
14. Neff P. Local existence and uniqueness for a geometrically exact membrane-plate with viscoelastic transverse shear resistance. Mathematical Methods in the Applied Sciences 2005; 28:1031-1060. DOI: 10.1002/mma.597 (Preprint 2364, http://wwwbib.mathematik.tu-darmstadt.de/Math-Net/Preprints/Listen/ pp04.html).
15. Le Dret H, Raoult A. From three-dimensional elasticity to nonlinear membranes. In Asymptotic Methods for Elastic Structures, Proceedings of the International Conference, Ciarlet PG, Trabucho L, Viano JM (eds). Walter de Gruyter: Berlin, 1995.
16. Miara B. Nonlinearly elastic shell models: a formal asymptotic approach. I. The membrane model. Archive for Rational Mechanics and Analysis 1998; 142:331-353.
17. Ciarlet PG, Sanchez-Palencia E. Ellipticity of bending and membrane shell equations. In Asymptotique Methods for Elastic Structures, Proceedings of the International Conference, Ciarlet PG, Trabucho L, Viano JM (eds). Walter de Gruyter: Berlin, 1995.
18. Le Dret H, Raoult A. The nonlinear membrane model as a variational limit of nonlinear three-dimensional elasticity. Journal de Mathimatiques Pures et Appliquées 1995; 74:549-578.
19. Haseganu E, Steigmann DJ. Analysis of partly wrinkled membranes by the method of dynamic relaxation. Computational Mechanics 1994; 14:596-614.
20. Higham NJ. Computing the nearest symmetric positive semi-definite matrix. Linear Algebra and its Applications 1988; 103:103-118.
21. Holzapfel G. Nonlinear Solid Mechanics. Wiley: New York, 2000.
22. Carstensen C, Weinberg K. An adaptive nonconforming finite element method for Reissner-Mindlin plates. International Journal for Numerical Methods in Engineering 2003; 56:2313-2330.
23. Weinberg K. An adaptive finite element approach for a mixed Reissner-Mindlin plate formulation. Computer Methods in Applied Mechanics and Engineering 2001; 190(37-38):4999-5008.
24. Hofmann KH, Morris SA. The Structure of Compact Groups. Studies in Mathematics. deGruyter: Berlin, 1998.
25. Wong YW, Pellegrino S. Wrinkled membranes. In Textile Composites and Inflatable Structures, Onate E, Kröplin B (eds). CIMNE: Barcelona, 2003.
26. Carstensen C, Weinberg K. Calculating the energy-norm FEM-error for Reissner-Mindlin plates without known reference solution. Computational Mechanics 2000; 26(6):566-570.