A Variational Approach to Plates on Elastic Foundations

  • N. S. V. Kameswara Rao
Conference paper


Approximate methods may have to be adopted for the solution of complex problems in solid mechanics. Vlasov’s variational method (1,2) is considered in this context because of its simplicity, computational economy and efficiency. The method simplifies the continuum problem into a discrete-continuum problem thus reducing the governing equations to ordinary differential equations (which can be easily solved), without losing any of the physical characteristics in the process of mathematical simplification. Further, the method is versatile enough to tackle problems involving non-homogeneity, anisotropy, arbitrary boundary conditions besides being computationally economic as compared to the Finite Element Method. The bending theory of plates on generalised elastic foundations is presented using this method. The elastic foundation is modelled as a discrete-continuum and general solutions of finite plates on such foundations have been obtained in terms of initial parameters. Application of the method of initial parameters to general plate configurations carrying arbitrary external loads and moments is discussed, thus emphasising the versatality, computational efficiency and adaptability of the same. Both static and dynamic analyses are discussed and few results are presented in non-dimensional form.


Initial Parameter Elastic Foundation Virtual Displacement Computational Economy Arbitrary Boundary Condition 
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  1. 1.
    Vlasov, V.Z., Leontev,U.N.: Beams, plates and shells on elastic foundations, (Translated from Russian), NASA TT F-357, 1966.MATHGoogle Scholar
  2. 2.
    Kameswara Rao, N.S.V.: Variational approach to beams and plates on elastic foundations, Ph.D. Thesis, I.I.T. Kanpur, 1969.Google Scholar
  3. 3.
    Kameswara Rao, N.S.V.: Variational approach to beams on elastic foundations, Journal of the Engineering Mechanics Division, Proceedings of the ASCE, 97,EM2, (April, 1971) 271–294.Google Scholar
  4. 4.
    Kameswara Rao, N.S.V.: Dynamic response of beams on generalised elastic foundations. Int. J. of Solids and Structures. 11,3, (March, 1975) 255–273.MATHCrossRefGoogle Scholar
  5. 5.
    Kerr, A.D.: Elastic and viscoelastic foundation models. Journal of Applied Mechanics, 31, Trans. ASME, (September, 1964) 491–498.ADSMATHCrossRefGoogle Scholar

Copyright information

© Springer Japan 1986

Authors and Affiliations

  • N. S. V. Kameswara Rao
    • 1
  1. 1.Department of Civil EngineeringIndian Institute of TechnologyKanpurIndia

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