Geodesic
Koiter shell governed by strongly monotone constitutive equations
International Journal of Applied Mathematics and Computer Science, Tome 14 (2004) no. 2, pp. 127-137

Voir la notice de l'article provenant de la source Library of Science

In this paper we use the theory of monotone operators to generalize the linear shell model presented in (Blouza and Le Dret, 1999) to a class of physically nonlinear models. We present a family of nonlinear constitutive equations, for which we prove the existence and uniqueness of the solution of the presented nonlinear model, as well as the convergence of the Galerkin method. We also present the physical discussion of the model.
Keywords: Koiter shell, physical nonlinearity, strongly monotone operators
Mots-clés : teoria Koitera, nieliniowość fizyczna, operator monotoniczny 
Kalita, P. Koiter shell governed by strongly monotone constitutive equations. International Journal of Applied Mathematics and Computer Science, Tome 14 (2004) no. 2, pp. 127-137. http://geodesic.mathdoc.fr/item/IJAMCS_2004_14_2_a0/
@article{IJAMCS_2004_14_2_a0,
     author = {Kalita, P.},
     title = {Koiter shell governed by strongly monotone constitutive equations},
     journal = {International Journal of Applied Mathematics and Computer Science},
     pages = {127--137},
     year = {2004},
     volume = {14},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IJAMCS_2004_14_2_a0/}
}
TY  - JOUR
AU  - Kalita, P.
TI  - Koiter shell governed by strongly monotone constitutive equations
JO  - International Journal of Applied Mathematics and Computer Science
PY  - 2004
SP  - 127
EP  - 137
VL  - 14
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/IJAMCS_2004_14_2_a0/
LA  - en
ID  - IJAMCS_2004_14_2_a0
ER  - 
%0 Journal Article
%A Kalita, P.
%T Koiter shell governed by strongly monotone constitutive equations
%J International Journal of Applied Mathematics and Computer Science
%D 2004
%P 127-137
%V 14
%N 2
%U http://geodesic.mathdoc.fr/item/IJAMCS_2004_14_2_a0/
%G en
%F IJAMCS_2004_14_2_a0

[1] Antman S.S. (1995): Nonlinear Problems of Elasticity. — New York: Springer-Verlag.

[2] Bernardou M. and Ciarlet P.G. (1976): Sur l’ellipticité du modéle lineaire de coques de W.T. Koiter, In: Computing Methods in Applied Sciences and Engineering (R. Glowinski and J.L. Lions, Eds.). — Heidelberg: Springer, Lect. Not. Econ., Vol. 134, pp. 89–136.

[3] Berne R.M. and Levy M.N. (1983): Physiology. — St. Louis: The C.V. Mosby Company.

[4] Blouza A. and Le Dret H. (1999): Existence and uniqueness for the linear Koiter model for shells with little regularity. — Quart. Appl. Math., Vol. 57, No. 2, pp. 317–337.

[5] Cemal Eringen A. (1962): Nonlinear Theory of Continuous Media.— New York: McGraw-Hill.

[6] Chapelle D. and Bathe K.J. (1998): Fundamental considerations for the finite element analysis of shell structures. — Comput. Struct., Vol. 66, No. 1, pp. 19–36.

[7] Ciarlet P.G. (2000): Mathematical Elasticity, Vol. III: Theory of Shells.—Amsterdam: Elsevier.

[8] Gajewski H., Gröger K. and Zacharias K. (1974): Nichtlineare operatorgleichungen und operatordifferentialgleichungen. —Berlin: Akademie-Verlag.

[9] Gaudiello A., Gustafsson B., Lefter C. and Mossino J. (2002): Asymptotic analysis for monotone quasilinear problems in thin multidomains. — Diff. Int. Eqns., Vol. 15, No. 5, pp. 623–640.

[10] Kalita P. (2003): Arterial wall modeled by physically nonlinear Koiter shell. — Proc. 15th Int. Conf. Computer Methods in Mechanics CMM-2003, Gliwice/Wisła, Poland, (published on CD-ROM).

[11] Kerdid N. and Mato Eiroa P. (2000): Conforming finite element approximation for shells with little regularity. — Comput. Meth. Appl. Mech. Eng., Vol. 188, No. 1–3, pp. 95–107.

[12] Koiter W.T. (1970): On the foundations of the linear theory of thin elastic shells. — Proc. Kon. Ned. Akad. Wetensch., Vol. B 73, pp. 169—195.

[13] Noll W. and Truesdell C. (1965): Encyclopedia of Physics, Vol. III/3: The Non-Linear Field Theories of Mechanics. — New York: Springer.

[14] Rudin W. (1973): Functional Analysis. —New York: Blaisdell.

[15] Schaefer R. and Sędziwy S. (1999), Filtration in cohesive soils: Mathematical model. — Comput. Assist. Mech. Eng. Sci., Vol. 6, No. 1, pp. 1–13.