Abstract
We consider the problem of modeling dynamic thin shells with thermal effects based on the intrinsic geometry methods of Michel Delfour and Jean-Paul Zolésio. This model relies on the oriented distance function which describes the geometry. Here we further develop the Kirchhoff-based shell model introduced in our previous work by subjecting the elastically and thermally isotropic shell to an unknown temperature distribution. This yields a fully-coupled system of four linear equations whose variables are the displacement of the shell mid-surface and the thermal stress resultants.
Paper written with financial support of the National Science Foundation under Grant DMS-0408565.
Chapter PDF
Similar content being viewed by others
References
M. Bernadou. Finite Element Methods for Thin Shell Problems. J. Wiley and Sons, 1996.
J. Cagnol, I. Lasiecka, C. Lebiedzik, and J.-R Zolésio. Uniform Stability in Structural Acoustic Models with Flexible Curved Walls J. Diff. Eqns. 186:88–121, 2003.
J. Cagnol and C. Lebiedzik. On the free boundary conditions for a shell model based on intrinsic differential geometry. Applicable Analysis. 83:607–633, 2004.
J. Cagnol and C. Lebiedzik. Optimal Control of a Structural Acoustic Model with Flexible Curved Walls. In Control and boundary analysis, Lect. Notes Pure Appl. Math., 240, Chapman & Hall/CRC, Boca Raton, FL, 2005.
M. C. Delfour and J.-P. Zolésio. Differential equations for linear shells: comparison between intrinsic and classical models In Advances in mathematical sciences: CRM’’s 25 years (Montreal, PQ, 1994), CRM Proc. Lecture Notes Amer. Math. Soc. Providence, RI, 1997.
M. C. Delfour and J.-P. Zolésio. Intrinsic differential geometry and theory of thin shells. To appear, 2006.
J. Lagnese and J.-L. Lions. Modelling, Analysis and Control of Thin Plates. Masson, Paris, 1988.
W. Nowacki. Thermoelasticity, 2nd Edition. Pergamon Press, New York, 1986.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 International Federation for Information Processing
About this paper
Cite this paper
Lebiedzik, C. (2006). Intrinsic Modeling of Linear Thermo-Dynamic Thin Shells. In: Ceragioli, F., Dontchev, A., Furuta, H., Marti, K., Pandolfi, L. (eds) Systems, Control, Modeling and Optimization. CSMO 2005. IFIP International Federation for Information Processing, vol 202. Springer, Boston, MA . https://doi.org/10.1007/0-387-33882-9_20
Download citation
DOI: https://doi.org/10.1007/0-387-33882-9_20
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-33881-1
Online ISBN: 978-0-387-33882-8
eBook Packages: Computer ScienceComputer Science (R0)