Structural Engineering and Mechanics

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On the theory of curved anisotropic plate

  • Received : 2005.09.22
  • Accepted : 2006.01.09
  • Published : 2006.04.20
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Abstract

A general theory which describes the elastic response of a curved anisotropic plate subjected to stretching and bending will be developed by considering the nonlinear effect that reflecting the non-flat geometry of the structure. By applying a newly derived $6{\times}6$ matrix constitutive relation between force resultants, moment resultants, mid-plane strains and deformed curvatures, the governing differential equations for a curved anisotropic plate is developed in the usual manner, namely, by consideration of the constitutive relation and equilibrium equations. Solutions are obtained for simply-supported boundary conditions and compared to corresponding solutions that neglecting the nonlinear effect in the analysis. The comparisons indicate that the nonlinear terms in the equations that caused by the curvature of the structure is crucial for the curved plate analysis. Under certain curved plate geometries the unreasonable results will be induced by neglecting the nonlinear effect in the analysis.

Keywords

References

  1. Ambartsumyan, S.A. (1964), Theory of Anisotropic Shells, Moscow, 1961, English Translation, NASA-TT-F-118
  2. Ambartsumyan, S.A. (1964), Theory of Anisotropic Shells, NASA Report TT F-118
  3. Bickford, W.B. (1998), Advance Mechanics of Materials, 1st ed. Addison Wesley Longman, Inc., Menlo Park
  4. Chaudhuri, R.A. (1986), 'Arbitrarily laminated, anisotropic cylindrical shell under internal pressure', AIAA J., 24(11), 1851-1858 https://doi.org/10.2514/3.9534
  5. Cheng, S. and Ho, B.P.C. (1963), 'Stability of heterogeneous aeolotropic cylindrical shells under combined loading', AlAA J., 1(4), 892-898
  6. Chiang, Y.C. (2005), 'The poisson effect on the curved beam analysis', Struct. Eng. Mech., 19(6), 707-720 https://doi.org/10.12989/sem.2005.19.6.707
  7. Dong, S.B., Pister, K.S. and Taylor, R.L. (1962), 'On the theory of laminated anisotropic shells and plates,' J. of the Aerospace Sci., 29, 969-975 https://doi.org/10.2514/8.9668
  8. Flugge, W. (1967), Stress in Shells, Springer, Berlin
  9. Gulati, S.T. and Essenberg, F. (1967), 'Effects of anisotropic in axisymmetric cylindrical shells', J. Appl. Mech., 34, 659-666 https://doi.org/10.1115/1.3607758
  10. Herakovich, C.T. (1998), Mechanics of Fibrous Composites, New York: John Wiley & Sons, Inc.
  11. Kjellmert, B. (1997), 'A Chebyshev collocation multidomain method to solve the Reissner-Mindlin equations for the transient response of an anisotropic plate subjected to impact', Int. J. Numer. Meth. Eng., 40, 3689-3702 https://doi.org/10.1002/(SICI)1097-0207(19971030)40:20<3689::AID-NME233>3.0.CO;2-E
  12. Koiter, W.T. (1959), 'A consistent first approximation in the general theory of thin elastic shells,' in Proc. of the IUTAM Symposium on The Theory of Thin Elastic Shells, Delft, 24-28 August, 1959, Edited by W.T. Koiter, North-Holland Publishing Co., Amsterdam, 12-33
  13. Kraus, H. (1972), Thin Elastic Shells: An Introduction to the Theoretical Foundations and the Analysis of Their Static and Dynamic Behavior, John Wiley and Sons, Inc.
  14. Lekhnitskii, S.G. (1986), Anisotropic Plates, Gordon and Breach Science Publishers, New York
  15. Novozhilov, V.V. (1959), The Theory of Thin Shells, Translated by Lowe, P.G, Edited by Radok, J.R.M. Groningen: P. Noordhoff
  16. Reddy, J.N. (1984), 'Exact solutions of moderately thick laminated shells', J. Eng. Mech., 110(5), 794-809 https://doi.org/10.1061/(ASCE)0733-9399(1984)110:5(794)
  17. Reddy, J.N. (2004), Mechanics of Laminated Composite Plates and Shells Theory and Analysis, 2nd Ed., CRC Press
  18. Reddy, J.N. and Wang, C.M. (2000), 'An overview of the relationships between solutions of the classical and shear deformation plate theories', Comp. Sci. Tech., 60, 2327-2335 https://doi.org/10.1016/S0266-3538(00)00028-2
  19. Sanders Jr., J.L. (1959), 'An improved first approximation theory for thin shells', NASA TR-R24
  20. Sokolnikoff, I.S. (1964), Tensor Analysis: Theory and Applications to Geometry and Mechanics of Continua, John Wiley and Sons, Inc.
  21. Swanson, S.R. (1997), Introduction to Design and Analysis with Advanced Composite Materials, Prentice-Hall, Inc.
  22. Timoshenko, S. and Woinowsky-Krieger, S. (1959), Theory of Plates and Shells, Second Edition, McGraw-Hill Book Company, Inc.
  23. Vinson, J.R. and Sierakowski, R.L. (1987), The Behavior of Structures Composed of Composite Materials, Kluwer Adademic Publishers
  24. Vlasov, V.Z. (1964), General Theory of Shells and Its Application to Engineering, Moscow-Leningrad, 1949, NASA Technical Translation NASA-TT-F-99
  25. Whitney, J.M. (1987), Structure Analysis of Laminated Anisotropic Plates, Technomic Publishing Co. Inc.
  26. Whitney, J.M. and Sun, C.-T. (1974), 'A refined theory for laminated anisotropic, cylindrical shells', J. Appl. Mech., 41(2), 471-476 https://doi.org/10.1115/1.3423312
  27. Zukas, J.A. and Vinson, J.R. (1971), 'Laminated transversely isotropic cylindrical shells', J. Appl. Mech., 38, 400-407 https://doi.org/10.1115/1.3408789

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