Publication Cover
Applicable Analysis
An International Journal
Volume 83, 2004 - Issue 6
48
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

On the Free Boundary Conditions for a Dynamic Shell Model Based on Intrinsic Differential Geometry

&
Pages 607-633 | Received 02 May 2003, Published online: 04 Sep 2006

References

  • Bernadou M 1996 Finite Element Methods for Thin Shell Problems, John Wiley and Sons Chichester
  • Bernadou M Boisserie JM 1982 The Finite Element Method for Thin Shell Problems, Birkhauser Boston
  • Bernadou M Ciarlet PG 1976 Sur l′ ellipticité du modèle linéare de coques de W.T. Koiter Computing Methods in Applied Sciences and Engineering 34 pp. 89–136 Lecture notes in economics and mathematical systems Springer-Verlag Berlin
  • Bernadou , M , Ciarlet , PG and Miara , B . 1994 . Existence theorems for two-dimensional linear shell theories . J. Elasticity , 34 : 111 – 138 .
  • Cagnol , J , Lasiecka , I , Lebiedzik , C and Zolésio , J-P . 2002 . Uniform stability in structural acoustic models with flexible curved walls . J. Differential Equations , 186 ( 1 ) : 88 – 121 .
  • Delfour M Zolèsio JP 2004 Intrinsic Differential Geometry and Theory of Thin Shells (to appear)
  • Delfour , MC and Zolésio , J-P . 1995 . A boundary differential equation for thin shells . Journal of Differential Equations , 119 ( 2 ) : 426 – 449 .
  • Delfour MC Zolésio J-P 1997 Differential equations for linear shells: comparison between intrinsic and classical models Advances in Mathematical Sciences: CRM's 25 years (Montreal, PQ, 1994) CRM Proc. Lecture Notes 11 pp. 481–491 Amer. Math. Soc. Providence RI
  • Germain P 1986 Mécanique 1 Ellipses Marketing Ecole Polytechnique France
  • Kirchhof G 1876 Vorlesungen uber Mathematische Physik, Mechanik Leipzig
  • Koiter WT August 1959 A consistent first approximation in the general theory of thin shells Proc. Symp. on Theory of Thin Elastic Shells pp. 12–33 (held in Delft)
  • Koiter , WT . 1970 . On the foundation of the linear theory of thin elastic shells . Proc. Kon. Nederl. Akad. Wetensch. , B73 : 169 – 195 .
  • Lagnese J 1989 Boundary Stabilization of Thin Plates, SIAM Philadelphia PA
  • Lagnese J Lions J-L 1988 Modelling Analysis and Control of Thin Plates, Volume 6 of Research in Applied Mathematics, Masson Paris
  • Love AEH 1934 The Mathematical Theory of Elasticity, Cambridge University Press Cambridge UK
  • Naghdi , PM . 1972 . The theory of shells and plates . Handbuch der Physik , VI : 425 – 640 .
  • Pazy , A . 1983 . Semigroups of linear operators and applications to partial differential equations . Applied Mathematical Sciences, Springer-Verlag , 44
  • Xiao Li-ming 1998 Asymptotic analysis of dynamic problems for linearly elastic shells—justification of equations for dynamic membrane shells Asymptotic Analysis 17 2 121 134 1998
  • Yao P-F 1997 On the Shallow Shell Equations, Institute of System Science, Chinese Academy of Science Beijin China (Preprint)
  • Yao , P-F . 2000 . Observability inequalities for shallow shells . SIAM J. Control , 38 : 1729 – 1756 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.