Koiter shell governed by strongly monotone constitutive equations

Piotr Kalita

International Journal of Applied Mathematics and Computer Science (2004)

  • Volume: 14, Issue: 2, page 127-137
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Kalita, Piotr. "Koiter shell governed by strongly monotone constitutive equations." International Journal of Applied Mathematics and Computer Science 14.2 (2004): 127-137. <http://eudml.org/doc/207684>.

@article{Kalita2004,
abstract = {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.},
author = {Kalita, Piotr},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {Koiter shell; physical nonlinearity; strongly monotone operators},
language = {eng},
number = {2},
pages = {127-137},
title = {Koiter shell governed by strongly monotone constitutive equations},
url = {http://eudml.org/doc/207684},
volume = {14},
year = {2004},
}

TY - JOUR
AU - Kalita, Piotr
TI - Koiter shell governed by strongly monotone constitutive equations
JO - International Journal of Applied Mathematics and Computer Science
PY - 2004
VL - 14
IS - 2
SP - 127
EP - 137
AB - 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.
LA - eng
KW - Koiter shell; physical nonlinearity; strongly monotone operators
UR - http://eudml.org/doc/207684
ER -

References

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  2. Bernardou M. and Ciarlet P.G. (1976): Sur l'ellipticite du modele lineaire de coques de W.T. Koiter, In: Computing Methods in Applied Sciences and Engineering (R. Glowinski andJ.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. Zbl1025.74020
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  7. Ciarlet P.G. (2000): Mathematical Elasticity, Vol. III: Theory of Shells. - Amsterdam: Elsevier. 
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  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. Zbl1034.35020
  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. Zbl0963.74062
  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. Zbl0213.27002
  13. Noll W. and Truesdell C. (1965): Encyclopedia of Physics, Vol. III3: The Non-Linear Field Theories of Mechanics. - New York: Springer. Zbl0779.73004
  14. Rudin W. (1973): Functional Analysis. - New York: Blaisdell. Zbl0253.46001
  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. Zbl0970.76098

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