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Structure of rod shell theories in Hilbert space

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Abstract

This paper builds symmetrically general theories of rods and shells under mathematical frame of “Hilbert Space”, and successfully obtains the error estimate to the system of theory.

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References

  1. Nordgren, R.P., A bound on the error in plate theory,Q. Appl. Math.,28 (1971), 587–595.

    MATH  MathSciNet  Google Scholar 

  2. Simmonds, J. G., An improved error estimate in the classical linear theory of plate bending,Q. Appl. Math.,29 (1971), 439–447.

    MATH  Google Scholar 

  3. Rychter, Z., A bound on the error in the linear theory of transversely isotropic plate bending,Acta Mechanica,34 (1984), 121–126.

    Article  Google Scholar 

  4. Rychter, Z., An improved error estimate for Reissner's plate theory.Int. J. Solids Struct.,24 (1986), 537–544.

    Article  MathSciNet  Google Scholar 

  5. Rychter, Z., Global error estimate in Reissner theory of thin elastic shells,Int. J. Engng. Sci.,26 (1988), 787–795.

    Article  MATH  MathSciNet  Google Scholar 

  6. Harro, G. Heuser,Functional Analysis, John Wiley & Sons Ltd (1982).

  7. Ruth, F. Curtain and A. J. Pritchard,Functional Analysis in Modern Applied Mathematics, Academic Press Inc. Ltd, London (1977).

    Google Scholar 

  8. Guo, Z. H.,Tensor (Theory and Application), Science Press (1988). (in Chinese)

  9. Huang, K. Z.,Tensor Analysis, Qinghua University Press (1986). (in Chinese)

  10. Su, B. Q.,Differential Geometry, People Education Press (1979). (in Chinese)

  11. Flugge, W.,Tensor Analysis and Continuum Mechanics, Springer-Verlag (1972).

  12. Guo, Z. H.,Nonlinear Elasticity Theory, Science Press (1980). (in Chinese)

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Communicated by Yang Gui-tong

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Quan-shui, Z., De-ping, Y. & Gu-quan, S. Structure of rod shell theories in Hilbert space. Appl Math Mech 13, 445–459 (1992). https://doi.org/10.1007/BF02450735

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  • DOI: https://doi.org/10.1007/BF02450735

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