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On a Problem of Thermal Stresses in the Theory of Cosserat Elastic Shells with Voids

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IUTAM Symposium on Relations of Shell Plate Beam and 3D Models

Part of the book series: IUTAM Bookseries ((IUTAMBOOK,volume 9))

Abstract

We consider a problem of thermal stresses in cylindrical Cosserat elastic shells made from a material with voids. The cylindrical shells have arbitrary cross-sections. The problem consists in finding the equilibrium of the shell under the action of a given temperature distribution. We assume that the temperature field is independent of the axial coordinate and we determine a closed-form solution expressed in terms of the displacement vector and porosity field.

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References

  1. Naghdi P M (1972) The Theory of Shells and Plates. In: C. Truesdell (ed), Handbuch der Physik, Vol. VI a/2, pp. 425–640, Springer-Verlag, Berlin Heidelberg New York

    Google Scholar 

  2. Rubin M B (2000) Cosserat Theories: Shells, Rods, and Points. Kluwer Academic Publishers, Dordrecht

    Google Scholar 

  3. Green A E, Naghdi P M (1979) On thermal effects in the theory of shells. Proc. R. Soc. Lond. A365: 161–190

    MathSciNet  Google Scholar 

  4. Bîrsan M (2006) On the theory of elastic shells made from a material with voids. Int. J. Solids Struct. 43: 3106–3123

    Article  Google Scholar 

  5. Ciarlet P G (2000) Mathematical Elasticity, Vol. III: Theory of Shells. North-Holland, Amsterdam

    Google Scholar 

  6. Bîrsan M (2008) Inequalities of Korn’s type and existence results in the theory of Cosserat elastic shells. J. Elasticity 90: 227–239

    Article  MATH  MathSciNet  Google Scholar 

  7. Bîrsan M (2006) Several results in the dynamic theory of thermoelastic Cosserat shells with voids. Mech. Res. Comm. 33: 157–176

    Article  MathSciNet  Google Scholar 

  8. Rubin M B, Benveniste Y (2004) A Cosserat shell model for interphases in elastic media. J. Mech. Phys. Solids 52: 1023–1052

    Article  MATH  MathSciNet  Google Scholar 

  9. Bîrsan M (2006) On a thermodynamic theory of porous Cosserat elastic shells. J. Therm. Stresses 29: 879–900

    Article  Google Scholar 

  10. Nunziato J W, Cowin S C (1979) A nonlinear theory of elastic materials with voids. Arch. Ration. Mech. An. 72: 175–201

    MATH  MathSciNet  Google Scholar 

  11. Capriz G, Podio-Guidugli P (1981) Materials with spherical structure. Arch. Ration. Mech. An. 75: 269–279

    MATH  MathSciNet  Google Scholar 

  12. Vekua I N, Rukhadze A K (1933) Torsion problem for a circular cylinder reinforced by a longitudinal circular rod (in Russian). Izv. Akad. Nauk SSSR 3: 1297–1308

    Google Scholar 

  13. Lomakin V A (1976) Theory of Nonhomogeneous Elastic Bodies (in Russian). MGU, Moscow

    Google Scholar 

  14. Hatiashvili G M (1983) Almansi-Michell Problems for Homogeneous and Composed Bodies (in Russian). Izd. Metzniereba, Tbilisi

    Google Scholar 

  15. Ieşan D (1987) Saint-Venant’s Problem. Lect. Notes Math., no. 1279, Springer-Verlag, Berlin

    Google Scholar 

  16. Bîrsan M (2004) The solution of Saint-Venant’s problem in the theory of Cosserat shells. J. Elasticity 74: 185–214

    Article  MATH  MathSciNet  Google Scholar 

  17. Bîrsan M (2006) Extension, bending and torsion of cylindrical Cosserat shells made from a porous elastic material. In: CD-ROM Proceedings of the 3rd European Conference on Computational Mechanics (Portugal, Lisbon, 5–8 June 2006), 18pp., ISBN 978-1-4020-4994-1, Springer, Dordrecht

    Google Scholar 

  18. Ieşan D (2007) Thermal stresses in inhomogeneous porous elastic cylinders. J. Therm. Stresses 30: 145–164

    Article  Google Scholar 

  19. Vrabie I I (2004) Differential Equations: An Introduction to Basic Concepts, Results and Applications. World Scientific, New Jersey

    Google Scholar 

  20. Ieşan D (2004) Thermoelastic Models of Continua. Kluwer Academic Publishers, Dordrecht Boston London

    Google Scholar 

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Bîrsan, M. (2008). On a Problem of Thermal Stresses in the Theory of Cosserat Elastic Shells with Voids. In: Jaiani, G., Podio-Guidugli, P. (eds) IUTAM Symposium on Relations of Shell Plate Beam and 3D Models. IUTAM Bookseries, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8774-5_6

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  • DOI: https://doi.org/10.1007/978-1-4020-8774-5_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-8773-8

  • Online ISBN: 978-1-4020-8774-5

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