On Questions of Existence in Shell Theory

Jump To References Section

Authors

  • Universite Pierre et Marie Curie 4, Place Jussieu 75230, Paris, Cedex 05 ,FR

Abstract

In this paper, we consider a modelization of the shell problem, known as Koiter's model. The description of this model is found at various stages of its development in Koiter (1966, 1970), Koiter and Simmonds (1972).

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Published

1976-12-01

How to Cite

Ciarlet, P. G. (1976). On Questions of Existence in Shell Theory. The Journal of the Indian Mathematical Society, 40(1-4), 131–143. Retrieved from https://informaticsjournals.co.in/index.php/jims/article/view/16618

 

References

BABUSKA, I. and A.K. Aziz (1972): Survey Lectures on the Mathematical Foundations of the Finite Element Method, in The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, 3-359 Academic Press, New York.

BERNADOU, M. and P.G. CIARLET (1976) : Sur 1'ellipticite du modele lineaire de coques de W.T. Koiter, to appear in the Proceedings of the Second International Symposium on Computing Methods in Applied Sciences and Engineering, I.R.I.A., Versailles, 15-19 December, 1975.

CIARLET, P.G. (1975): Lectures on the Finite Element Method, Tata Institute of Fundamental Research, Bombay.

CIARLET, P.G. (1976a) : Numerical Analysis of the Finite Element Method, Seminaire de Mathematiques Superieures, Presses de l'Untversite de Montreal.

CIARLET, P.G. (1976b) : Conforming finite element methods for the shell problem, to appear in the Proceedings of the Conference on the Mathematics of Finite Elements and Applications, Brunei University, 07-10 April, 1975.

COUTRIS, N. (1973) : Flexions elastique et elastoplastique d'une coque mince /. Mecanique 12, 463-475.

GORDEZIANI, D.G. (1974) : On the solvability of some boundary value problems for a variant of the theory of thin shells, Dokl. Akad. Nauk SSSR 215 No. 6, 677-680.

GOUYON, R. (1963) : Calcul Tensoriel, Vuibert, Paris.

HORMANDER L. (1964): Linear Partial Differential Operators, Springer-Verlag, Berlin.

JOHN, F. (1965): Estimates for the derivatives of the stresses in a thin shell and interior shell equations, Comm. Pure and Appl. Math. 18, 235-267.

KOITER, W.T. (1966) : On the nonlinear theory of thin elastic shells, Proc. Kon. Ned. Akad. Wet. 569, 1-54.

KOITER, W.T. (1970) : On the foundations of the linear theory of thin elastic shells. I, II, Proc. Kon. Ned. Akad. Wet. 573, 169-195.

KOITER, W.T. and J.C. SIMMONDS (1972) : Foundations of shell theory, Proceedings of the 13th International Congress of Theoretical and Applied Mechanics, Moscow, 150-176.

KOLAKOWSKI, K. and M. DRYJA (1974) : A boundary value problem for equations of elastic cylindrical shell, Bulletin de VAcadimie Polonaise des Sciences, Sirie des Sciences Techniques XXII, No. 11, 37-42.

LELONG-FERRAND, J. (1963) : Geomitrie Differentielle, Masson, Paris.

LICHNEROWICZ, A. (1967) : Elements de Calcul Tensoriel, Armand Colin, Paris (8th edition).

MIYOSHI, T. (1973) : Finite element method of mixed type and its convergence in linear shell problems, Kumamoto J. Sci. (Math) 10, 35-58.

MOAN, T. (1974) : A note on the convergence of finite element approximations for problems formulated in curvilinear coordinate systems, Computer Methods in Applied Mechanics and Engineering 3, 209-235.

NAGHDI, P.M. (1963) : Foundations of elastic shell theory, in Progress in Solid Mechanics, Vol. 4, 1-90, North-Holland, Amsterdam.

NAGHDI, P.M. (1972) : The Theory of Shells and Plates, Handbuch der Physik, Springer-Verlag, Berlin.

NOVOZHILOV, V.V. (1970) : Thin Shell Theory, Wolters-Noordhoff.

ODEN, J.T. and J.N. REDDY(1976): An Introduction to the Mathematical Theory of Finite Elements, Wiley Interscience, New York.

ROUGEE, P. (1969): Equilibre desCoques Elastiques Minces lnhomogenes en Theorie non Lineaire, Thesis, University of Paris.

SHOIKET, B.A. (1974): On existence theorems in linear shell theory, PMM, 38 567571 [English translation : Journal of Applied Mathematics and Mechanics 38 (1974), 527-531].

STRANG, G. and G.J. Fix, (1973) : An Analysis of the Finite Element Method, PrenticeHall, Englewood Cliffs.

TIMOSHENKO, S. and WOINOWSKY-KRIEGER, S. (1959) : Theory of Plates and Shells, McGraw-Hill.

VALIRON, G. (1950) : Equations Fonctionnelles. Applications, Masson, Paris (2nd edition).

VEKUA I.N. (1965) : Theory of thin shallow shells of variable thickness, Akad. Nauk Gruzin. SSR Trudy Tbilissi Mat. Inst. Razmadze 30, 3-103.

WASHIZU, K. 1968 : Variational methods in Elasticity and Plasticity, Pergamon.