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Deflection relationships between classical and third-order plate theories

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Summary

In this paper the differential relationship between the deflections of the classical Kirchhoff and third-order Reddy plate theories is developed, and it is used to determines the relationship between the deflections of polygonal plates with simply supported boundary conditions. As an example, the deflection of a simply supported rectangular plate using the third-order plate theory is obtained from the relationship developed herein. The relationship indicates that the third-order theory yields virtually the same solution as the first-order theory for simply supported rectangular plates.

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References

  1. Reddy, J. N.: Mechanics of laminated composite plates: theory and analysis. Boca Raton: CRC Press, 1997.

    Google Scholar 

  2. Reddy, J. N.: A simple higher-order theory for laminated composites plates. J. Appl. Mech.51, 745–752 (1984).

    Google Scholar 

  3. Reddy, J. N.: Energy and variatitional methods in applied mechanics. New York: John Wiley, 1984.

    Google Scholar 

  4. Wang, C. M., Alwis, W. A. M.: Simply supported polygonal Mindlin plate deflections using Kirchhoff plates. J. Eng. Mech.121, 1383–1385 (1995).

    Google Scholar 

  5. Wang, C. M., Lee, K. H.: Deflection and stress-resultants of axisymmetric Mindlin plates in terms of corresponding Kirchhoff solutions. Int. J. Mech. Sci.38, 1179–1185 (1996).

    Google Scholar 

  6. Wang, C. M.: Relationships between Mindlin and Kirchhoff bending solutions for tapered circular and annular plates. Eng. Struct.19, 255–258 (1997).

    Google Scholar 

  7. Marcus, H.: Die Theorie elastischer Gewebe. Berlin: Springer, 1932.

    Google Scholar 

  8. Conway, H. D.: Analogies between the buckling and vibration of polygonal plates and membranes. Can. Aeron. J.6, 263 (1960).

    Google Scholar 

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Author notes

  1. J. N. Reddy

    Present address: Department of Mechanical Engineering, Texas A&M University, 77843-3123, College Station, Texas, USA

  2. C. M. Wang

    Present address: Department of Civil Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore

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    1. J. N. Reddy
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    2. C. M. Wang
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    Reddy, J.N., Wang, C.M. Deflection relationships between classical and third-order plate theories. Acta Mechanica 130, 199–208 (1998). https://doi.org/10.1007/BF01184311

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    • DOI: https://doi.org/10.1007/BF01184311

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