Концентрація динамічних напружень у пружному просторі з двоперіодичним масивом еліптичних тріщин: Fìz.-mat. model. ìnf. tehnol. 2020, 28:18-25

• Date: 2020
• Main Author: Zhbadynskyi, Igor
• Format: Article
• Language: Ukrainian
• Published: Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України 2020
• Subjects: еліптичні тріщини; динамічні коефіцієнти інтенсивності напружень; метод граничних інтегральних рівнянь; періодична функція Гріна; метод відображень
• Online Access: https://www.fmmit.lviv.ua/index.php/fmmit/article/view/130
• Journal Title: Physico-mathematical modeling and informational technologies

Normal incidence of the plane time-harmonic longitudinal wave on double-periodic array of coplanar elliptical cracks, which are located in 3D infinite elastic space is considered. Corresponding symmetric wave scattering problem is reduced to a boundary integral equation for the displacement jump across the crack surfaces in a unit cell by means of periodic Green’s function, which is presented in the form of Fourier integrals. A regularization technique for this Green’s function involving special lattice sums in closed forms is adopted, which allows its effective calculation in a wide range of wave numbers. The boundary integral equation is correctly solved by using the mapping method. The frequency dependencies of mode-I stress intensity factor in the vicinity of the crack front points for periodic distances in the system of elliptical cracks are revealed. References Mykhas’kiv, V., Zhbadynskyi, I., Zhang, C. (2010). Elastodynamic analysis of multiple crack problem in 3-D bi-materials by a BEM. Int. J. Numer. Meth. Biomed. Eng., 26, 1934–1946. DOI https://doi.org/10.1002/cnm.1285 Mykhailova, I. I., Menshykov, O. V., Guz, I. A. (2011). Cracks’ closure in 3-D fracture dynamics: The effect of relative location of two coplanar cracks/ Arch. Appl. Mech., 81, 1215–1230. DOI https://doi.org/10.1007/s00419-010-0481-0 Zhbadynskii, I. Ya. (2016). Interaction of one-periodic disk-shape cracks under an incident elastic harmonic wave. Mechanics of Solids, 51(1), 127–134. DOI https://doi.org/10.3103/s002565441601012x Zhbadynskyi, I. Ya. (2018). Vzaiemodiia odnoperiodychnykh podatlyvykh dyskovykh eliptychnoi formy vkliuchen pry padinni pruzhnoi harmonichnoi khvyli. Dop. NAN Ukrainy, 10, 37—43. Mykhas’kiv, V. V., Zhbadynskyi, I. Ya., Zhang, Ch. (2019). On propagation of time-harmonic elastic waves through a double-periodic array of penny-shaped cracks. European Journal of Mechanics. A Solids, 73, 306—317. DOI https://doi.org/10.1016/j.euromechsol.2018.09.009 Remizov, M. Yu, Sumbatyan, M. A. (2017). Three-dimensional one-mode penetration of elastic waves through a doubly periodic array of cracks. Math. Mech. Solid, 23, 636—650. DOI https://doi.org/10.1177/1081286516684902 Zhbadynskyi, I. Ya. (2007). Vyznachennia koefitsiienta intensyvnosti napruzhen vidryvu u bimaterialnomu tili z eliptychnoiu trishchynoiu pid nestatsionarnym navantazhenniam. Mat. metody i fiz.-mekh. polia, 50(1), 161–167.