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Solution of Stress-Strain Problems for Complex-Shaped Plates in a Refined Formulation

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A numerical-analytical approach to solving problems on the stress–strain state of quadrangular plates of complex shape is proposed. The governing system of equations is presented in new orthogonal coordinates using transformations that take into account the plate geometry. A two-dimensional boundary-value problem, which is described by a system of partial differential equations derived with the spline-collocation method, is reduced to a one-dimensional one that is solved by the stable numerical discrete-orthogonalization method. The numerical results obtained for plates in the form of a trapezium and parallelogram are compared with the data obtained by other methods. The approach makes it possible to calculate deflections of quadrangular plates of complex shape made of anisotropic materials

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Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterova St, Kyiv, 03057, Ukraine

    A. Ya. Grigorenko, S. A. Pankrat’ev & S. N. Yaremchenko

Authors
  1. A. Ya. Grigorenko
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  2. S. A. Pankrat’ev
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  3. S. N. Yaremchenko
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Correspondence to A. Ya. Grigorenko.

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Translated from Prikladnaya Mekhanika, Vol. 53, No. 3, pp. 104–112, May–June, 2017.

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Grigorenko, A.Y., Pankrat’ev, S.A. & Yaremchenko, S.N. Solution of Stress-Strain Problems for Complex-Shaped Plates in a Refined Formulation. Int Appl Mech 53, 326–333 (2017). https://doi.org/10.1007/s10778-017-0814-6

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  • DOI: https://doi.org/10.1007/s10778-017-0814-6

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