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Investigation of the three-dimensional stressed state in elastic plates with circular holes

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The stress-strain state (SSS) of an isotropic elastic plate weakened by a circular hole is determined in the three-dimensional statement. We propose a numerical-analytic method for the solution of three-dimensional problems of the theory of elasticity. The vector of displacements is represented via three independent harmonic functions. The spectral representation of the perturbed SSS is obtained in the form of a series in nonorthogonal eigenfunctions. The coefficients of the series are determined from the condition of the most exact validity of the boundary conditions on the surface of the hole. The estimate of the error of realization of the boundary conditions is obtained. The distribution of stresses is numerically analyzed depending on Poisson’s ratio and the radius of the hole.

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Authors and Affiliations

  1. Pidstryhach Institute for Problems in Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv, Ukraine

    V. P. Revenko

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  1. V. P. Revenko
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Correspondence to V. P. Revenko.

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Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 45, No. 5, pp. 71–76, September–October, 2009.

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Revenko, V.P. Investigation of the three-dimensional stressed state in elastic plates with circular holes. Mater Sci 45, 688–695 (2009). https://doi.org/10.1007/s11003-010-9232-1

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  • DOI: https://doi.org/10.1007/s11003-010-9232-1

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