Варіаційний метод однорідних розв’язків у осесиметричній задачі теорії пружності для скінченного циліндра: Fìz.-mat. model. ìnf. tehnol. 2018, 27:118-129

• Дата: 2019
• Автори: Chekurin, Vasyl, Postolaki, Lesya
• Формат: Стаття
• Мова: Українська
• Опубліковано: Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України 2019
• Теми: варіаційний метод однорідних розв’язків; осесиметрична задача теорії пружності; функція Лява; скінченний циліндр; метод редукції
• Онлайн доступ: https://www.fmmit.lviv.ua/index.php/fmmit/article/view/122
• Назва журналу: Physico-mathematical modeling and informational technologies

Variational method of homogeneous solutions for solving of axisymmetric elasticity problem for a finite cylinder with homogenous conditions on his surface for the stresses given on one end, and on the other — displacements is developed. A numerical study of the convergence of the solution of the problem was performed using the reduction method. Application of the developed method to determine the stress components distributions in the finite cylinder, an end of which is rigidly clamped and to the opposite one normal force are applied, has been exemplified in the paper. References Agarwal, V. K. (1978). Axisymmetric solution of the end-problem for a semi-infinite elastic circular cylinder and its application to joined dissimilar cylinders under uniform tension. International Journal of Engineering Science, 16(12), 985-998.https://doi.org/10.1016/0020-7225(78)90056-3 Sburlati, R. (2009). Three-dimensional analytical solution for an axisymmetric biharmonic problem. J. Elasticity, 95(1), 79-97.https://doi.org/10.1007/s10659-009-9195-3 Chau, K. T., Wei, X. X. (2000). Finite solid circular cylinders subjected to arbitrary surface load. Part I. Analytic solution. Int. J. Solids Struct., 37(40), 5707-5732.https://doi.org/10.1016/S0020-7683(99)00289-9 Chau, K. T., Wei, X. X. (2000). Finite solid circular cylinders subjected to arbitrary surface load. Part II. Application to double-punch test. Int. J. Solids Struct., 37(40), 5733-5744.https://doi.org/10.1016/S0020-7683(99)00290-5 Tokovyi, Yu. V. (2010). Osesymetrychni napruzhennia v skinchennomu pruzhnomu tsylindri pid diieiu normalnoho tysku, rivnomirno rozpodilenoho po chastyni bichnoi poverkhni. Prykl. problemy mekh. i mat., 8, 144-151. Meleshko, V. V., Tokovyi, Yu. V., Barber, D. R. (2010). Osesymetrychni temperaturni napruzhennia u pruzhnomu izotropnomu tsylindri skinchennoi dovzhyny. Mat. metody ta fiz.-mekh. polia, 53(1), 120-137. Popov, G. Ya., Protserov, Yu. S. (2016). Axisymmetric problem for an elastic cylinder of finite length with fixed lateral surface with regard for its weight. J. Math. Sci., 212(1), 67–82.https://doi.org/10.1007/s10958-015-2649-1 Vihakl, V. M., Yasinskyy, A. V., Tokovyy, Y. V., Rychahivskyy, A. V. (2007). Exact solution of the axisymetric thermoelasticity problem for a long cylinder subjected to varying with-respect-to-length loads. J. Mech. Behav. Materials, 18(2), 141-148.https://doi.org/10.1515/JMBM.2007.18.2.141 Protserov, Yu. S. (2017). Axisymmetric problem of the theory of elasticity for a hollow cylinder of finite length with regard for its weight. Journal of Mathematical Sciences, 226(2), 160-174.https://doi.org/10.1007/s10958-017-3527-9 Chekurin, V. F., Postolaki, L. I. (2014). Variational method of homogeneous solutions in axisymmetric elasticity problems for a semiinfinite cylinder. Journal of Mathematical Sciences, 201(2), 175-189.https://doi.org/10.1007/s10958-014-1982-0 Chekurin, V., Postolaki, L. (2016). Application of the least square method in axisymmetric biharmonic problems. Mathematical Problems in Engineering..https://doi.org/10.1155/2016/3457649 Chekurin, V F., Postolaki, L.I. (2016). Variatsiinyi metod odnoridnykh rozviazkiv u osesymetrychnii zadachi teorii pruzhnosti dlia kuskovo-odnoridnoho tsylindra. Fizyko-matematychne modeliuvannia ta informatsiini tekhnolohii, 24, 118-129. Chekurin, V. F., Postolaki, L. I. (2015). A variational method of homogeneous solutions for axisymmetric elasticity problems for cylinder. Mathematical modeling and computing, 2(2), 128–132.https://doi.org/10.23939/mmc2015.02.128 Timoshenko, S. P., Guder, Dzh. (1975). Teoriya uprugosti. M.: Nauka.