ВІСЕСИМЕТРИЧНА ЗАДАЧА КРУЧЕННЯ ЗРІЗАНОГО КОНУСА ЗІ СФЕРИЧНОЮ ТРІЩИНОЮ
DOI:
https://doi.org/10.30890/2567-5273.2024-35-00-006Ключові слова:
зрізаний конус, сферична тріщина, коефіцієнт інтенсивності напружень, інтегральне перетворення, метод ортогональних многочленівАнотація
У роботі розглядається задача кручення усіченого конуса з внутрішньою сферичною тріщиною. Метою дослідження є визначення напружено-деформованого стану конуса за наявності тріщини і прикладеного вісесиметричного дотичного навантаження на поверхню. Для вирMetrics
Посилання
Das, S.Ch. (1956) 'On the stress in composite truncated cone due to shearing stress on the curved surface', Indian Journal of Theoretical Physics, no. 4, pp. 82–92.
Low, R.B. and Weiss, H.F. (1961) 'On a mixed boundary value problem for an infinite elastic cone', Zeitschrift für angewandte Mathematik und Physik (ZAMP), vol. 13, no. 3, pp. 232–242.
Thompson, T.R. and Little, R.W. (1970) 'End effects in a truncated semi-infinite cone', Quarterly Journal of Mechanics and Applied Mathematics, vol. 23, no. 2, pp. 185–196.
Nuller, B.M. (1972) 'Torsion of an elastic space with a semi-infinite conical crack', Izvestiya Akademii Nauk SSSR, Mekhanika Tverdogo Tela, no. 1, pp. 150–152.
Budayev, B., Morozov, N., and Narbut, M. (1994) 'Torsion of a circular cone with static and dynamic loading', Journal of Applied Mathematics and Mechanics, vol. 58, no. 6, pp. 1097–1100.
Popov, G.Ya. (2003) 'On one method for obtaining integral transforms using in construction precise solutions to mathematical physics boundary-value problems', Matematicheskie Metody Fiziko-Mekhanicheskikh Poly, vol. 46, no. 3, pp. 74–89.
Popov, G.Ya. (2005) 'Specifications and additions to the paper "On one method for obtaining integral transforms using in construction precise solutions to mathematical physics boundary-value problems"', Matematicheskie Metody Fiziko-Mekhanicheskikh Poly, vol. 48, no. 3, pp. 75–81.
Popov, G.Ya. (2005) 'Axisymmetric problems of the theory of elasticity for a truncated hollow cone', Journal of Applied Mathematics and Mechanics, vol. 69, no. 3, pp. 417–426.
Vaisfel'd, N.D., Popov, G.Ya., and Reut, V.V. (2013) 'The axisymmetric mixed problem of elasticity theory for a cone clamped along its side surface with an attached spherical segment', Journal of Applied Mathematics and Mechanics, vol. 77, no. 1, pp. 70–78.
Vaisfel'd, N.D., Popov, G.Ya., and Reut, A.V. (2014) 'Axisymmetric problem of stressed state for a twice truncated cone', Journal of Mathematical Sciences, vol. 201, no. 2, pp. 229–244.
Popov, G.Ya. (2000) 'The problem of the stressed state of an elastic cone weakened by cracks', Journal of Applied Mathematics and Mechanics, vol. 64, no. 2, pp. 337–348.
Popov, G. and Vaysfel'd, N. (2009) 'The stress concentration in the neighborhood of the spherical crack inside the infinite elastic cone', Operator Theory: Advances and Applications, vol. 191, pp. 173–186.
Popov, G. and Vaysfel'd, N. (2010) 'The solution of Mitchell's problem for the elastic infinite cone with a spherical crack', Mathematical Problems in Engineering, vol. 2010, Article ID 652814, pp. 321–338.
Vaisfel'd, N.D. (2002) 'Nonstationary problem of torsion for an elastic cone with spherical crack', Materials Science, vol. 38, no. 5, pp. 698–708.
Mysov, K. and Vaysfeld, N. (2020) 'The dynamical stress concentration near a spherical crack in a twice-truncated elastic cone', Procedia Structural Integrity, vol. 28, pp. 352–357.
Mysov, K. and Vaysfeld, N. (2021) 'The dynamical stress concentration near a cone-shaped crack in a twice-truncated elastic cone', Procedia Structural Integrity, vol. 33, pp. 365–370.
Vaysfeld, N.D. and Misov, K.D. (2023) 'Wave field of a double-truncated spherically layered cone under torsional load', International Applied Mechanics, vol. 59, no. 6, pp. 734–741.
Popov, G.Ya. (1982) The elastic stress concentration around dies, cuts, thin inclusions and reinforcements (in Russian). Moscow: Nauka.
Bateman, H. and Erdélyi, A. (1953) Higher Transcendental Functions, vol. 1. New York: McGraw-Hill.
Prudnikov, A.P., Brychkov, Yu.A., and Marichev, O.I. (1981) Integrals and Series (in Russian). Moscow: Nauka.
Protserov, Yu. and Vaysfeld, N. (2017) 'Torsion problems of finite cylinders weakened by ring-shaped cracks', Procedia Structural Integrity, vol. 3, pp. 526–544.
Abramowitz, M. and Stegun, I.A. (1964) Handbook of Mathematical Functions. Washington, D.C.: U.S. Government Printing Office.
Опубліковано
Як цитувати
Номер
Розділ
Ліцензія
Авторське право (c) 2024 Автори
Ця робота ліцензується відповідно до Creative Commons Attribution 4.0 International License.
