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Journal of Elasticity

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01-04-2014

Strong Convergence Results for the Asymptotic Behavior of the 3D-Shell Model

Authors: D. Chapelle, A. Collin

Published in: Journal of Elasticity | Issue 2/2014

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Abstract

We revisit the asymptotic convergence properties—with respect to the thickness parameter—of the earlier-proposed 3D-shell model. This shell model is very attractive for engineering applications, in particular due to the possibility of directly using a general 3D constitutive law in the corresponding finite element formulations. We establish strong convergence results for the 3D-shell model in the two main types of asymptotic regimes, namely, bending- and membrane-dominated behavior. This is an important achievement, as it completely substantiates the asymptotic consistency of the 3D-shell model with 3D linearized isotropic elasticity.

previous article On Deformations with the Same Principal Stretches

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See www.adina.com, in particular.

Ahmad, S., Irons, B.M., Zienkiewicz, O.C.: Analysis of thick and thin shell structures by curved finite elements. Int. J. Numer. Methods Eng. 2, 419–451 (1970) CrossRef

Auricchio, F., Lovadina, C., Madureira, A.L.: An asymptotically optimal model for isotropic heterogeneous linearly elastic plates. Modél. Math. Anal. Numér. 38, 877–897 (2004) CrossRefMATHMathSciNet

Bathe, K.J.: Finite Element Procedures. Prentice Hall, Englewood Cliffs (1996)

Bernadou, M.: Finite Element Methods for Thin Shell Problems. Wiley, New York (1996) MATH

Bischoff, M., Ramm, E.: On the physical significance of higher order kinematic and static variables in a three-dimensional shell formulation. Int. J. Solids Struct. 37, 6933–6960 (2000) CrossRefMATH

Chapelle, D., Bathe, K.J.: Fundamental considerations for the finite element analysis of shell structures. Comput. Struct. 66, 19–36 (1998) CrossRefMATH

Chapelle, D., Bathe, K.J.: The mathematical shell model underlying general shell elements. Int. J. Numer. Methods Eng. 48(2), 289–313 (2000) CrossRefMATHMathSciNet

Chapelle, D., Bathe, K.J.: The Finite Element Analysis of Shells—Fundamentals, 2nd edn. Springer, Berlin (2011) CrossRefMATH

Chapelle, D., Ferent, A., Bathe, K.J.: 3D-shell finite elements and their underlying model. Math. Models Methods Appl. Sci. 14(1), 105–142 (2004) CrossRefMATHMathSciNet

10.

Chapelle, D., Ferent, A., Le Tallec, P.: The treatment of “pinching locking” 3D-shell elements. ESAIM: M2AN, 37, 143–158 (2003) CrossRefMATH

11.

Ciarlet, P.G.: Mathematical Elasticity—Volume III: Theory of Shells. North-Holland, Amsterdam (2000)

12.

Dauge, M., Yosibash, Z.: Boundary layer realization in thin elastic 3D domains and 2D hierarchic plate models. Int. J. Solids Struct. 37, 2443–2471 (2000) CrossRefMATH

13.

Delfour, M.C.: Intrinsic P(2,1) thin shell model and Naghdi’s models without a priori assumption on the stress tensor. In: Hoffmann, K.H., Leugering, G., Tröltzsch, F. (eds.) Optimal Control of Partial Differential Equations, pp. 99–113. Birkhäuser, Basel (1999) CrossRef

14.

Green, A.E., Zerna, W.: Theoretical Elasticity, 2nd edn. Clarendon, Oxford (1968) MATH

15.

Kim, D.N., Bathe, K.J.: A 4-node 3D-shell element to model shell surface tractions and incompressible behavior. Comput. Struct. 86(21–22), 2027–2041 (2008) CrossRef

16.

Koiter, W.T.: On the nonlinear theory of thin elastic shells. Proc. K. Ned. Akad. Wet., Ser. B, Phys. Sci. 69, 1–54 (1965) MathSciNet

17.

Lions, J.L.: Perturbations Singulières dans les Problèmes aux Limites et en Contrôle Optimal. Springer, Berlin (1973) MATH

18.

Paumier, J.-C., Raoult, A.: Asymptotic consistency of the polynomial approximation in the linearized plate theory. ESAIM Proc. 2, 203–213 (1997) CrossRefMATHMathSciNet

19.

Pitkäranta, J., Matache, A.M., Schwab, C.: Fourier mode analysis of layers in shallow shell deformations. Comput. Methods Appl. Mech. Eng. 190, 2943–2975 (2001) ADSCrossRefMATH

20.

Rössle, A., Bischoff, M., Wendland, W., Ramm, E.: On the mathematical foundation of the (1,1,2)-plate model. Int. J. Solids Struct. 36(14), 2143–2168 (1999) CrossRefMATH

21.

Sanchez-Hubert, J., Sanchez-Palencia, E.: Coques Elastiques Minces—Propriétés Asymptotiques. Masson, Paris (1997) MATH

Title: Strong Convergence Results for the Asymptotic Behavior of the 3D-Shell Model
Authors: D. Chapelle
A. Collin
Publication date: 01-04-2014
Publisher: Springer Netherlands
Published in: Journal of Elasticity / Issue 2/2014
Print ISSN: 0374-3535
Electronic ISSN: 1573-2681
DOI: https://doi.org/10.1007/s10659-013-9452-3

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On Deformations with the Same Principal Stretches

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