Torsion of transversely isotropic plate with a non-circular cylindrical hole. (English. Russian original) Zbl 1462.74106
Int. Appl. Mech. 56, No. 4, 445-461 (2020); translation from Prikl. Mekh., Kiev 56, No. 4, 61-77 (2020).
Summary: The problem of the stress state of an unbounded transversely isotropic plate with a noncircular cylindrical hole is solved by expanding functions into Fourier-Legendre series in the thickness coordinate and using the boundary shape perturbation method. The surface of the hole is free from external forces, and the plate is subject to constant torques at infinity. The stress distribution in the vicinity of the hole with elliptical boundary or triangular boundary with rounded corners in the midsurface is analyzed. The dependence of stresses on the relative thickness of the plate and elastic constants is established.
MSC:
| 74K20 | Plates |
Keywords:
infinite transversely isotropic plate; torsion of the plate; stress state; noncircular hole; elliptical boundary; triangular boundaryReferences:
| [1] | Vekua, IN, Theory of thin shallow shells of variable thickness, Tr. Tbilis. Mat. Inst., 30, 3-103 (1965) · Zbl 0166.20904 |
| [2] | Guz, AN; Nemish, YN, Boundary-Shape Perturbation Method in Continuum Mechanics [in Russian] (1989), Kyiv: Vyshcha Shkola, Kyiv · Zbl 0699.73017 |
| [3] | Nemish, YN; Khoma, IY, Bending of nonthin transversally isotropic plates with curvilinear openings, Int. Appl. Mech., 24, 1, 80-88 (1988) |
| [4] | Polozhiy, HM, Equations of Mathematical Physics [in Ukrainian] (1959), Kyiv: Radyanska Shkola, Kyiv · Zbl 0085.08102 |
| [5] | Guz, ÀN; Chernyshenko, IS; Chekhov, VN, Theory of Thin Shells Weakened by Holes, Vol. 1 of the five-volume series Methods of Shell Design [in Russian] (1980), Naukova Dumka: Kyiv, Naukova Dumka · Zbl 0524.73072 |
| [6] | Abbas Ibrahim, A., Fractional order gn model on thermoelastic interaction in an infinite fibre-reinforced anisotropic plate containing a circular hole, J. Comput. Theor. Nanosci., 11, 2, 380-384 (2014) · doi:10.1166/jctn.2014.3363 |
| [7] | D. I. Bardzokas, D. V. Kushnir, and L. A. Filstinskii, “Dynamic problems of the theory of elasticity for layers and semilayers with cavities,” Acta Mechanica, No. 208, 81-95 (2009). · Zbl 1397.74082 |
| [8] | Burniston, EE, On the extension of on infinite elastic plate containing an axisymmetric hole, J. Appl. Mech., 39, 2, 507-512 (1972) · Zbl 0235.73033 · doi:10.1115/1.3422708 |
| [9] | F. Darwish, M. Gharaibeh, and G. Tashtoush, “A modified equation for the stress concentration factor in countersunk holes,” Eur. J. Mech. A/Solids., No. 36, 94-103 (2012). · Zbl 1347.74086 |
| [10] | Ding, H.; Chen, W.; Zhang, L., Elasticity of Transversely Isotropic Materials (2006), Dordrecht: Springer, Dordrecht · Zbl 1101.74001 |
| [11] | Fellers, JI; Soler, AI, Approximate Solution of the Finite Cylinders Problem Using Legendre Polynomials, AIAA J., 8, 11, 2037-2048 (1970) · Zbl 0221.73023 · doi:10.2514/3.6043 |
| [12] | L. A. Filshtinskii, U. O. Kovalev, and E. S. Ventsel, “Solution of the elastic boundary value problem for a layer with tunnel stresses raisers,” Int. J. Solids Struct., No. 39, 6385-6402 (2002). · Zbl 1032.74632 |
| [13] | Folias, ES; Wang, JJ, On the three-dimensional stress field around a circular hole in a plate of arbitrary thickness, Comput. Mech., 6, 5, 379-391 (1990) · doi:10.1007/BF00350419 |
| [14] | Grigorenko, YM; Grigorenko, AY; Zakhariichenko, LI, Analysis of the influence of the geometrical parameters of elliptic cylindrical shells with variable thickness on their stress-strain state, Int. App. Mech., 54, 2, 155-162 (2018) · doi:10.1007/s10778-018-0867-1 |
| [15] | Grigorenko, YM; Pankratiev, SA; Yaremchenko, SN, Influence of orthotropy on stress-strain state of quadrangular plates of different shapes, Int. Appl. Mech., 55, 2, 199-210 (2019) · doi:10.1007/s10778-019-00950-6 |
| [16] | Khoma, IY; Proshchenko, TM, Tension and shear of a transversely isotropic piezoceramic plate with a circular hole with mixed conditions on flat sides, Int. Appl. Mech., 53, 6, 704-715 (2017) · doi:10.1007/s10778-018-0852-8 |
| [17] | Khoma, IY; Proshchenko, TM, The stress state of a transversely isotropic plate with curvilinear hole for a given splitting force at the boundary surface, Int. Appl. Mech., 55, 4, 434-448 (2019) · doi:10.1007/s10778-019-00963-1 |
| [18] | Kotousov, A.; Wang, CH, Three-dimensional stress constraint in an elastic plate with a notch, Int. J. Solids Struct., 39, 16, 4311-4326 (2009) · Zbl 1045.74033 · doi:10.1016/S0020-7683(02)00340-2 |
| [19] | Rezaeepazhand, J.; Jafari, M., Stress concentration in metallic plates with special shaped cutout, Int. J. Mech. Scien., 52, 1, 96-102 (2010) · doi:10.1016/j.ijmecsci.2009.10.013 |
| [20] | Z. Yang, C. Kim, C. Cho, and N. G. Beom, “The concentration of stress and strain in finite thickness elastic plate containing a circular hole,” Int. J. Solids Struct., No. 45, 713-731 (2008). · Zbl 1167.74435 |
| [21] | Z. Yang, “The stress and strain concentration of an elliptical hole in an elastic plate of finite subjected to tensile stress,” Int. J. Fract., 43-44 (2009). · Zbl 1273.74485 |
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