Skip to main content
SpringerLink
Log in

On Constitutive Restrictions in the Resultant Thermomechanics of Shells with Interstitial Working

  • Chapter
  • First Online:
Shell-like Structures

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 15))

  • 2026 Accesses

Abstract

We analyse the restrictions imposed by the recently derived refined, resultant 2D entropy inequality on the forms of 2D constitutive equations of viscous shells with heat conduction and of thermoelastic shells. Due to the presence of additional non-classical surface fields, the entropy inequality does allow the constitutive equations to capture some kinematic and thermal longer-range spatial and temporal interactions. We also propose several forms of the 2D kinetic constitutive equations.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Simmonds, J.G.: The nonlinear thermodynamical theory of shells: descent from 3-dimensions without thickness expansions. In: Axelrad, E.L., Emmerling, F.A. (eds.) Flexible Shells, Theory and Applications, pp. 1–11. Springer, Berlin (1984)

    Google Scholar 

  2. Pietraszkiewicz, W., Chróścielewski, J., Makowski, J.: On dynamically and kinematically exact theory of shells. In: Pietraszkiewicz, W., Szymczak, C. (eds.) Shell Structures: Theory and Applications., pp. 163–167. Taylor & Francis, London (2005)

    Google Scholar 

  3. Pietraszkiewicz, W.: Refined resultant thermomechanics of shells. Int. J. Eng. Sci. (2011) (submitted)

    Google Scholar 

  4. Pietraszkiewicz, W.: On non-linear shell thermodynamics with interstitial working. In: Wilmański, K., Jędrysiak, J., Michalak, B. (eds.) Mathematical Methods in Continuum Mechanics. Politechnika \({\L}\)ódzka, \({\L}\)ódź (2011) (in print)

    Google Scholar 

  5. Dunn, J.E., Serrin, J.: On the thermodynamics of interstitial working. Arch. Rational Mech. Anal. 85, 95–133 (1985)

    Google Scholar 

  6. Dunn, J.E.: Interstitial working and a non-classical continuum. In: Serrin, E. (ed.) New Perspectives in Thermodynamics, pp. 187–222. Springer, Berlin (1986)

    Google Scholar 

  7. Truesdell, C., Toupin, R.: The Classical Field Theories. In: Flügge, S. (ed.) Handbuch der Physik, Band III/1., Springer, Berlin (1960)

    Google Scholar 

  8. Truesdell, C., Noll, W.: The Non-Linear Field Theories of Mechanics. In: Flügge, S. (ed.) Handbuch der Physik, Band III/3., Springer, Berlin (1965)

    Google Scholar 

  9. Coleman, B.D., Noll, W.: The thermodynamics of elastic materials with heat conduction and viscosity. Arch. Rational Mech. Anal. 13(1), 167–178 (1963)

    Article  Google Scholar 

  10. Eremeyev, V.A., Pietraszkiewicz, W.: Phase transitions in thermoelastic and thermoviscoelastic shells. Arch. Mech. 61(1), 125–152 (2009)

    Google Scholar 

  11. Chróścielewski J., Makowski J., Pietraszkiewicz W. (2004) Statics and Dynamics of Multi-Shells: Non-Linear Theory and the Finite Element Method. Institute of Fundamental Technological Research Press (in Polish). Warsaw

    Google Scholar 

  12. Cosserat, E., Cosserat, F.: Théorie des Corps Deformables. Hermann et Fils, Paris (1909)

    Google Scholar 

  13. Müller, I., Ruggeri, T.: Rational Extended Thermodynamics. 2nd edn. Springer, New York (1998)

    Google Scholar 

  14. Zhilin, P.A.: Basic equations of non-classical theory of elastic shells. Dinamika i Prochnost’ Mashin, Trudy Leningr. Polit. In-ta 386, 29–46 (1982) (in Russian)

    Google Scholar 

  15. Altenbach, H., Zhilin, P.A.: Theory of elastic simple shells. Advances in Mechanics 11, 107–148 (1988) (in Russian)

    Google Scholar 

  16. Eremeyev, V.A., Zubov, L.M.: Mechanics of Elastic Shells. 2nd edn. Nauka, Moskva (2008) (in Russian)

    Google Scholar 

  17. Zhilin, P.A.: Mechanics of deformable directed surfaces. Int. J. Solids Struct. 12(9-10), 635–648 (1976)

    Article  Google Scholar 

  18. Chróścielewski, J., Makowski, J., Pietraszkiewicz, W.: Non-linear dynamics of flexible shell structures. Comp. Assisted Mech. Eng. Sci. 9, 341–357 (2002)

    Google Scholar 

  19. Gurtin, M.E., Murdoch, A.I.: A continuum theory of elastic material surfaces. Arch. Rational Mech. Anal. 57, 291–323 (1975)

    Article  Google Scholar 

Download references

Acknowledgments

This research was supported by the Polish Ministry of Science and Education under grant No. N506 254237.

Author information

Authors and Affiliations

  1. Institute of Fluid-Flow Machinery of the Polish Academy of Sciences, ul. Gen. J. Fiszera 14, 80-952, Gdańsk, Poland

    Wojciech Pietraszkiewicz

Authors
  1. Wojciech Pietraszkiewicz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wojciech Pietraszkiewicz .

Editor information

Editors and Affiliations

  1. Magdeburg, Institut für Mechanik, Otto-von-Guericke-Universität, Universitätsplatz 2, Magdeburg, 30106, Sachsen-Anhalt, Germany

    Holm Altenbach

  2. Halle-Wittenberg, Martin-Luther-Universität, Kurt-Mothes-Str. 1, Halle, 06120, Germany

    Victor A. Eremeyev

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Pietraszkiewicz, W. (2011). On Constitutive Restrictions in the Resultant Thermomechanics of Shells with Interstitial Working. In: Altenbach, H., Eremeyev, V. (eds) Shell-like Structures. Advanced Structured Materials, vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21855-2_18

Download citation

Publish with us

Policies and ethics

Search

Navigation