Advertisement

Intrinsic Modeling of Linear Thermo-Dynamic Thin Shells

  • C. Lebiedzik
Conference paper
Part of the IFIP International Federation for Information Processing book series (IFIPAICT, volume 202)

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.

keywords

Intrinsic shell model dynamic thermoelasticity 

References

  1. [1]
    M. Bernadou. Finite Element Methods for Thin Shell Problems. J. Wiley and Sons, 1996.Google Scholar
  2. [2]
    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.CrossRefGoogle Scholar
  3. [3]
    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.MATHMathSciNetCrossRefGoogle Scholar
  4. [4]
    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.Google Scholar
  5. [5]
    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.Google Scholar
  6. [6]
    M. C. Delfour and J.-P. Zolésio. Intrinsic differential geometry and theory of thin shells. To appear, 2006.Google Scholar
  7. [7]
    J. Lagnese and J.-L. Lions. Modelling, Analysis and Control of Thin Plates. Masson, Paris, 1988.MATHGoogle Scholar
  8. [8]
    W. Nowacki. Thermoelasticity, 2nd Edition. Pergamon Press, New York, 1986.Google Scholar

Copyright information

© International Federation for Information Processing 2006

Authors and Affiliations

  • C. Lebiedzik
    • 1
  1. 1.Department of MathematicsWayne State UniversityDetroitUSA

Personalised recommendations