The problem of the stress state of a transversely isotropic plate with a curved hole is solved by expanding the unknown functions into Fourier–Legendre series in the thickness coordinate and using the boundary-shape perturbation method. Numerical results for plates with elliptic, square, and triangular holes are analyzed
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References
V. T. Grinchenko and A. F. Ulitko, “An exact solution of the Kirsch problem,” Int. Appl. Mech., 6, No. 5, 455–461 (1970).
O. M. Guz, “An approximate method for determining the stress concentration around curved holes in shells,” Prikl. Mekh., 8, No. 6, 605–612 (1962).
A. N. Guz and Yu. N. Nemish, Boundary-Shape Perturbation Method in Continuum Mechanics [in Russian], Vyshcha Shkola, Kyiv (1989).
À. N. Guz, I. S. Chernyshenko, V. N. Chekhov, et al., Theory of Thin Shells Weakened by Holes, Vol. 1 of the five-volume series Methods of Shell Design [in Russian], Naukova Dumka, Kyiv (1980).
D. I. Bardzokas, D. V. Kushnir, and L. A. Filshtinskii, “Dynamic problems of the theory of elasticity for layers and semilayers with cavities,” Acta Mech., 208, 81–95 (2009).
P. Cicala, “Sulla teoria elastica della plate soltile,” Giorngenio Civile, 97, No. 4, 238–256 (1959).
L. A. Fil’stinskii, U. D. Kovalev, and E. S. Vensel, “Solution of the elastic boundary value problem for a layer with tunnel stress raisers,” Int. J. Solids Struct., 39, 6385–6402 (2002).
E. S. Folias and J. S. Wang, “On the three-dimensional stress fields around a circular hole in a plate of arbitrary thickness,” Comp. Mech., 6, No. 5, 379–391 (1990).
A. E. Green, “Three-dimensional stress systems in isotropic plates,” Trans. Roy. Soc. London, Ser. A., 240, No. 285, 561–597 (1948).
I. Yu. Khoma, “On one technique of constructing the general solution to equilibrium equations for nonthin plates,” Int. Appl. Mech., 37, No. 4, 484–492 (2001).
I. Yu. Khoma, “Tension of a nonthin transversely isotropic plate with a noncircular cylindrical cavity,” Int. Appl. Mech., 42, No. 11, 1285–1297 (2006).
I. Yu. Khoma and O. A. Starygina, “Influence of elastic properties on the stress state of a nonthin transversely isotropic plate with a circular hole,” Int. Appl. Mech., 48, No. 1, 67–79 (2012).
I. Yu. Khoma, “Analytical solution of the equilibrium equations for nonthin electroelastic transversely isotropic plates polarized through the thickness,” Int. Appl. Mech., 50, No. 4, 430–445 (2014).
L. P. Khoroshun and L. V. Nazarenko, “Deformation and damage of composites with anisotropic components (review),” Int. Appl. Mech., 49, No. 4, 388–455 (2013).
L. P. Khoroshun and L. V. Nazarenko, “Nonlinear deformation properties of composites with transversely isotropic components,” Int. Appl. Mech., 50, No. 3, 253–262 (2014).
A. Kotousov and C. H. Wang, “Three-dimensional stress constraint in an elastic plate with a notch,” Int. J. Solids Struct., 39, No. 16, 4314–4326 (2002).
E. Sternberg, “Three-dimensional stress constraint in the theory of elasticity,” Appl. Mech. Rev., 11, No. 1, 1–4 (1958).
C. H. Wang, L. R. F. Rose, R. Callinan, and A. A. Baker, “Thermal stresses in a plate with a circular reinforcement,” Int. J. Solids Struct., 36, No. 33, 4577–4599 (2000).
Zh. Yang, “The stress and strain concentrations of an elliptical hole in an elastic plate of finite thickness subjected to tensile stress,” Int. J. Fract., 155, 43–44 (2009).
Zh. Yang, Kim Ch-Boo, Ch. Chjo, and N. G. Beom, “The concentration of stress and strain in finite thickness elastic plate containing a circular hole,” Int. J. Solids Struct., 45, 713–731 (2008).
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Translated from Prikladnaya Mekhanika, Vol. 51, No. 4, pp. 112–124, July–August 2015.
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Khoma, I.Y., Dashko, O.G. Stress State of a Nonthin Transversely Isotropic Plate with a Curved Hole. Int Appl Mech 51, 461–473 (2015). https://doi.org/10.1007/s10778-015-0707-5
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DOI: https://doi.org/10.1007/s10778-015-0707-5