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Abstrakty
The bending problem of an infinite, piecewise homogeneous, isotropic plate with circular interfacial zone and two coaxial radial cracks is solved on the assumption of crack closure along a line on the plate surface. Using the theory of functions of a complex variable, complex potentials and a superposition of plane problem of the elasticity theory and plate bending problem, the solution is obtained in the form of a system of singular integral equations, which is numerically solved after reducing to a system of linear algebraic equations by the mechanical quadrature method. Numerical results are presented for the forces and moments intensity factors, contact forces between crack faces and critical load for various geometrical and mechanical task parameters.
Czasopismo
Rocznik
Tom
Strony
16--21
Opis fizyczny
Bibliogr. 23 poz., rys., wykr.
Twórcy
autor
- Faculty of Mechanical Engineering, Department of Mechanics and Applied Computer Science Application, Bialystok University of Technology, ul. Wiejska 45 C, 15-351 Bialystok, Poland
autor
- Faculty of Mechanics and Mathematics, Department of Mechanics, Ivan Franko National University of L’viv, Universytetska St. 1, L’viv, 79000, Ukraine
autor
- Faculty of Mechanics and Mathematics, Department of Mechanics, Ivan Franko National University of L’viv, Universytetska St. 1, L’viv, 79000, Ukraine
autor
- Faculty of Applied Mathematics and Informatics, Department of Programming, Ivan Franko National University of L’viv, Universytetska St. 1, L’viv, 79000, Ukraine
autor
- Faculty Training Specialists Battle (Operational) Software, Department of Engineering Mechanics, Hetman Petro Sahaidachnyi National Army Academy, Heroes of Maidan Street, 32, L’viv, Ukraine
Bibliografia
- 1. Bäcker D., Kuna M., Häusler C. (2015), Eigenfunctions of crack problems in the Mindlin plate theory, ZAMM – Journal of Applied Mathematics and Mechanics, 95(8), 763–777.
- 2. Dempsey J. P., Shekhtman I. I., Slepyan L. I. (1998), Closure of a through crack in a plate under bending, International Journal of Solids and Structures, Vol. 35, No. 31-32, 4077–4089.
- 3. Hsieh M. C., Hwu C. (2002), Anisotropic elastic plates with holes/cracks/inclusions subjected to out-of-plane bending moments, International Journal of Solids and Structures, 39 (19), 4905–4925
- 4. Kuz’ I. S., Моrоz O. I., Kuz’ O. N. (2019), Strength of elastoplastic plates containing square holes (inclusions) and cuts (thin inclusions) under uniaxial tension, Materials Science, Vol. 54, No. 4, 603–609.
- 5. Kwon Y. W.(1989),Finite analysis of crack closure in plate bending. Computers and Structures, Vol. 32, No. 4, 1439–1445.
- 6. Liu Z., Chen X., Yu D., Wang X. (2018), Analysis of semi-elliptical surface cracks in the interface of bimaterial plates under tension and bending, Theoretical and Applied Fracture Mechanics, 93, 155–169.
- 7. Maksymovych O., Illiushyn O. (2017), Stress calculation and optimization in composite plates with holes based on the modifiedintegral equation method, Engineering Analysis with BoundaryElements, 83, 180–187.
- 8. Muskhelishvili N. I. (1966), Some basic problems of the mathematical theory of elasticity (in Russian), Nauka, Moscow.
- 9. Nguyen, V. T., Hwu, C. (2018), Multiple holes, cracks, and inclusions in anisotropic viscoelastic solids, Mechanics of Time-Dependent Materials, 22(2), 187–205.
- 10. Nielsen C. V., Legarth B. N., Niordson C. F. (2012), Extended FEM modeling of crack paths near inclusions, International Journal for Numerical Methods in Engineering, 89(6), 762–785.
- 11. Opanasovych V. K., Slobodyan M. S. (2007), Bending of a piecewise homogeneous plate with straightinterfacial crack with contactingfaces (in Ukrainian), Mathematical Methods and Physicomechanical Fields, 50(1), 168–177.
- 12. Opanasovych V. K., Yatsyk I. M., Sulym H. T. (2012), Bending of Reissner’s plate containing a through-the-thickness crack by concentrat ed moments taking into account the width of a contact zone of its faces, Journal of Mathematical Science, 187(5), 620–634.
- 13. Osadchuk V. A. (1985), Stress-strain state and limit equilibrium of cracked shells (in Russian), Naukova dumka, Kyiv.
- 14. Panasyuk V. V., Savruk M. P., Datsyshyn A. P. (1976), Stress propagation near the cracks in plates and shells (in Russian), Naukova dumka, Kyiv.
- 15. Prusov I. A. (1962), Some problems of the thermoelasticity (in Russian), Belarus. Univ., Minsk.
- 16. Prusov I. A. (1975), The method of conjugation in the theory of plates (in Russian), Belarus. Univ., Minsk.
- 17. Shao-Tzu C., Li H. (2017), Boundary-based finite element method for two-dimensional anisotropic elastic solids with multiple holes and cracks, Engineering Analysis with Boundary Elements, 79, 13–22.
- 18. Shatsky I. P. (1988), Bending of a plate weakened by a crack with contacting faces (in Ukrainian), Rep. of AS of USSR, Series Phys. Math. and Tech. Sci., 7, 49–51.
- 19. Shiah, Y-C., Hwu, C., Yao, J. J. (2019), Boundary element analysis of the stress intensity factors of plane interface cracks between dissimilarly adjoined anisotropic materials,Engineering Analysis with Boundary Elements, 106, 68–74.
- 20. Sulym H., Opanasovych V., Slobodian M., Bilash O. (2018), Combined Bending with Tension of Isotropic Plate with Crack Considering Crack Banks Contact and Plastic Zones at its Tops, Acta Mechanica et Automatica, Vol. 12, No. 2(44), 91–95.
- 21. Sulym H., Opanasovych V., Slobodian M., Yarema Y. (2018), Biaxial Loading of a Plate Containing a Hole and Two Co-Axial Through Cracks, Acta Mechanica et Automatica, Vol. 12, No. 3(45), 237–242.
- 22. Wang X., Nasebe N. (2000), Bending of a thin plate containing a rigid inclusion and a crack, Engineering Analysis with Boundary Elements, 24(2), 145–153.
- 23. Young M. J., Sun C. T.(1992),Influence of crack closure on the stress intensity factor in bending plates – A classical plate solution, International Journal of Fracture, 55, 81–93.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-fd294091-7ffc-41fb-816a-ba5eb5f7290f