Skip to main content

On Shear Deformation Plate Solutions: Relationship to The Classical Solutions

  • Chapter
Book cover Advances in the Mechanics of Plates and Shells

Part of the book series: Solid Mechanics and its Applications ((SMIA,volume 88))

  • 563 Accesses

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.00
Price excludes VAT (USA)
  • Compact, lightweight 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. Reissner, E., “On the theory of bending of elastic plates,” Journal of Mathematical Physics, 23, 184–191 (1944).

    MATH  MathSciNet  Google Scholar 

  2. Reissner, E., “The effect of transverse shear deformation on the bending of elastic plates,” Journal of Applied Mechanics, 12, 69–77 (1945).

    MathSciNet  Google Scholar 

  3. Kromm, A., “Verallgemeinerte Theorie der Plattenstatik,” Ing.-Arch., 21 (1953).

    Google Scholar 

  4. Kromm, A., “Über die Randquerkräfte bei gestützten Platten.,” Z. angew. Math. Mech., 35 (1955).

    Google Scholar 

  5. Pant, V., Theories of Elastic Plates, Noordhoff, Leyden, Netherlands (1975).

    Google Scholar 

  6. Reddy, J. N., Energy and Variational Methods in Applied Mechanics, John Wiley and Sons, New York, 1984.

    MATH  Google Scholar 

  7. Reddy, J. N., Mechanics of Laminated Composite Plates: Theory and Analysis, CRC Press, Boca Raton, Florida (1997).

    MATH  Google Scholar 

  8. Reddy, J. N., Theory and Analysis of Elastic Plates, Taylor & Francis, Philadelphia, PA (1999).

    Google Scholar 

  9. Basset, A. B., “On the extension and flexure of cylindrical and spherical thin elastic shells,” Phil. Trans. Royal Soc., (London) Ser. A, 181(6), 433–480 (1890).

    MATH  Google Scholar 

  10. Hildebrand, F. B., Reissner, E., and Thomas, G. B., “Notes on the foundations of the theory of small displacements of orthotropic shells,” NACA TN-1833, Washington, D.C. (1949).

    Google Scholar 

  11. Hencky, H., “Über die Berucksichtigung der Schubverzerrung in ebenen Platten,“ Ing. Arch., 16, 72–76 (1947).

    Article  MATH  MathSciNet  Google Scholar 

  12. Mindlin, R. D., “Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates,” Journal of Applied Mechanics, Transactions of ASME, 18, 31–38 (1951).

    MATH  Google Scholar 

  13. Reddy, J. N., “A simple higher-order theory for laminated composite plates,” Journal of Applied Mechanics, 51, 745–752 (1984).

    Article  MATH  Google Scholar 

  14. Reddy, J. N., “A general non-linear third-order theory of plates with moderate thickness,” International Journal of Non-Linear Mechanics, 25(6), 677–686 (1990).

    Article  MATH  Google Scholar 

  15. Vlasov, B. F., “Ob uravneniyakh teovii isgiba plastinok (On the Equations of the Theory of Bending of Plates),” Izv. Akd. Nauk SSR, OTN, 4, 102–109 (1958).

    Google Scholar 

  16. Jemielita, G., “Techniczna Teoria Plyt Srednieej Grubbosci (Technical theory of plates with moderate thickness)”, Rozprawy Insynierskie (Engineering Transactions), Polska Akademia Nauk. 23(3), 483–499 (1975).

    MATH  Google Scholar 

  17. Schmidt, R., “A refined nonlinear theory for plates with transverse shear deformation,” Journal of the Industrial Mathematics Society, 27(1), 23–38 (1977).

    MATH  Google Scholar 

  18. Krishna Murty, A. V., “Higher order theory for vibration of thick plates,” AIAA Journal, 15(12), 1823–1824 (1977).

    MATH  Google Scholar 

  19. Reddy, J. N., “A small strain and moderate rotation theory of laminated anisotropic plates,” Journal of Applied Mechanics, 54, 623–626 (1987).

    MATH  Google Scholar 

  20. Levinson, M., “An accurate, simple theory of the statics and dynamics of elastic plates”, Mechanics Research Communications, 7(6), 343–350 (1980).

    Article  MATH  Google Scholar 

  21. Wang, C. M., Reddy, J. N., and Lee, K. H., Shear Deformable Beams and Plates. Relationships with Classical Solutions, Elsevier, U.K., 2000.

    MATH  Google Scholar 

  22. Reddy, J. N., Wang, C. M., Lim, G. T., and Ng, K. H., “Bending solutions of the Levinson beams and plates in terms of the classical theories,” Int. J. Solids & Structures, in review.

    Google Scholar 

  23. Reddy, J. N. and Wang, C. M., “Deflection relationships between classical and third-order plate theories”, Acta Mechanica, 130(3–4), 199–208 (1998).

    MathSciNet  MATH  Google Scholar 

  24. Wang, C. M., “Allowance for prebuckling deformations in buckling load relationship between Mindlin and Kirchhoff simply supported plates of general polygonal shape”, Engineering Structures, 17(6), 413–418 (1995).

    Google Scholar 

  25. Wang, C. M., Discussion on “Postbuckling of moderately thick circular plates with edge elastic restraint”, J. Engng. Mech., ASCE, 122(2), 181–182 (1996).

    Google Scholar 

  26. Wang, C. M. and Reddy, J. N., “Buckling load relationship between Reddy and Kirchhoff plates of polygonal shape with simply supported edges”, Mechanics Research Communications, 24(1), 103–108 (1997).

    Article  Google Scholar 

  27. Wang, C. M., Xiang, Y., and Kitipornchai, S., “Buckling solutions of rectangular Mindlin plates under uniform shear”, Journal of Engineering Mechanics, 120(11), 2462–2470 (1994).

    Google Scholar 

  28. Wang, C. M., “Buckling of polygonal and circular sandwich plates” AIAA Journal, 33(5) 962–964 (1995).

    Article  MATH  Google Scholar 

  29. Wang, C. M., “Natural frequencies formula for simply supported Mindlin plates”, Trans. ASME, Journal of Vibration and Acoustics, 116(4), 536–540 (1994).

    Google Scholar 

  30. Wang, C. M., “Vibration frequencies of simply supported polygonal sandwich plates via Kirchhoff solutions”, Journal of Sound and Vibration, 190(2), 255–260 (1996).

    Article  Google Scholar 

  31. Wang, C. M., Kitipornchai, S. and Reddy, J. N., “Relationship between vibration frequencies of Reddy and Kirchhoff polygonal plates with simply supported edges”, ASME Journal of Vibration and Acoustics 122(1), 77–81 (2000).

    Google Scholar 

  32. Wang, C. M., Wang, C., and Ang, K. K., “Vibration of Initially Stressed Reddy Plates on a Winkler-Pasternak Foundation”, Journal of Sound and Vibration, 204(2), 203–212 (1997).

    Article  Google Scholar 

  33. Wang, C. M., Lim, G. T., Reddy, J. N., and Lee, K. H., “Relationships between bending solutions of Reissner and Mindlin plate theories”, Engineering Structures, to appear.

    Google Scholar 

  34. Reddy, J. N., “On locking-free shear deformable beam finite elements”, Computer Meth. Appl. Mech. Engng., 149, 113–132 (1997).

    MATH  Google Scholar 

  35. Reddy, J. N., Wang, C. M. and Lam, K. Y., “Unified finite elements based on the classical and shear deformation theories of beams and axisymmetric circular plates”, Communications in Numerical Methods in Engineering, 13, 495–510 (1997).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Kluwer Academic Publishers

About this chapter

Cite this chapter

Reddy, J.N., Wang, C.M. (2001). On Shear Deformation Plate Solutions: Relationship to The Classical Solutions. In: Durban, D., Givoli, D., Simmonds, J.G. (eds) Advances in the Mechanics of Plates and Shells. Solid Mechanics and its Applications, vol 88. Springer, Dordrecht. https://doi.org/10.1007/0-306-46954-5_17

Download citation

  • DOI: https://doi.org/10.1007/0-306-46954-5_17

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-6785-7

  • Online ISBN: 978-0-306-46954-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics