On the solution of the problem of axial compression of an elastic cylinder with specified ends displacement conditions
- Авторлар: Popov A.L.1,2, Vatulyan A.O.3, Chelyubeev D.A.1, Bukhalov V.I.1,4
-
Мекемелер:
- Ishlinskii Institute for Problems in Mechanics, Russian Academy of Sciences
- National research Moscow state University of civil engineering
- Southern Federal University
- A. Lyulka Experimental Design Bureau, subsidiary of PJSC “UEC-UMPO”
- Шығарылым: № 2 (2025)
- Беттер: 179-195
- Бөлім: Articles
- URL: https://journals.rcsi.science/1026-3519/article/view/295940
- DOI: https://doi.org/10.31857/S1026351925020109
- EDN: https://elibrary.ru/annjtr
- ID: 295940
Дәйексөз келтіру
Аннотация
A new scheme of approximate solution of the problem of axial compression of an elastic cylinder with one movable and the other fixed end with a free lateral surface is presented, refining the known solution obtained using separation of variables when averaging conditions over stresses on the lateral surface of the cylinder. The refinement is made by successive removal of discrepancies: first, in the stress distributions on the lateral surface of the cylinder, then in the radial displacements along the ends and further in the axial displacement of the movable end. Comparison with the results of numerical solution of the problem by the finite element method for different values of the Poisson ratio and different combinations of overall dimensions of the cylinder showed the effectiveness of the proposed approach.
Негізгі сөздер
Авторлар туралы
A. Popov
Ishlinskii Institute for Problems in Mechanics, Russian Academy of Sciences; National research Moscow state University of civil engineering
Email: aovatulyan@sfedu.ru
Ресей, Moscow; Moscow
A. Vatulyan
Southern Federal University
Хат алмасуға жауапты Автор.
Email: aovatulyan@sfedu.ru
Ресей, Rostov-on-Don
D. Chelyubeev
Ishlinskii Institute for Problems in Mechanics, Russian Academy of Sciences
Email: aovatulyan@sfedu.ru
Ресей, Moscow
V. Bukhalov
Ishlinskii Institute for Problems in Mechanics, Russian Academy of Sciences; A. Lyulka Experimental Design Bureau, subsidiary of PJSC “UEC-UMPO”
Email: vlad.buhalov@yandex.ru
Ресей, Moscow; Moscow
Әдебиет тізімі
- Filon L.N.G. On the elastic equilibrium of circular cylinders under certain practical systems of load // Philos. Trans. R. Soc. Lond. A198. 1902. P. 147–233. https://doi.org/10.1098/rspl.1901.0056
- Sirsat A.V., Padhee S.S. Analytic solution to isotropic axisymmetric cylinder under surface loadings problem through variational principle // Acta Mech. 2024. V. 235. P. 2013–2027. https://doi.org/10.1007/s00707-023-03825-7
- Pickett G. Application of the Fourier Method to the Solution of Certain Boundary Problems in the Theory of Elasticity // J. Appl. Mech. 1944. V. 11. Iss. 3. P. 176–182. https://doi.org/10.1115/1.4009381
- Prokopov V.K. Axisymmetric problem of elasticity theory for an isotropic cylinder // Trudy LPI. 1950. № 2. P. 286–303 (in Russian).
- Valov G.M. On the axisymmetric deformation of a solid circular cylinder of finite length // Mech. of Solids. 1962. V. 26. Iss. 4. P. 650–667.
- Blair J.M., Veeder J.I. The Elastic Deformation of a Circular Rod of Finite Length for an Axially Symmetric End Face Loading // J. Appl. Mech. 1969. V. 36. P. 241–246. https://doi.org/10.1115/1.3564615
- Meleshko V.V. Equilibrium of an elastic finite cylinder: Filon’s problem revisited // J. Eng. Math. 2003. V. 46. P. 355–376. https://doi.org/10.1007/BF00043957
- Benthem J.P., Minderhoud P. The problem of the solid cylinder compressed between rough rigid stamps // Int. J. Solids Struct. 1972. V. 8. P. 1027–1042. https://doi.org/10.1016/0020-7683(72)90067-4
- Chau K.T., Wei X.X. Finite solid circular cylinders subjected to arbitrary surface load. Part I – Analytic solution // Int. J. Solids Struct. 2000. V. 37. P. 5707–5732. https://doi.org/10.1016/S0020-7683(99)00289-9
- Gent A.N., Lindley P.B. The compression of bonded rubber blocks // Proc. Inst. Mech. Eng. 1959. V. 173. P. 111–122. https://doi.org/10.1243/PIME_PROC_1959_173_022_02
- Chalhoub M.S., Kelly J.M. Analysis of infinite-strip-shape base isolator with elastomer bulk compression // J. Eng. Mech. 1991. V. 117. P. 1791–1805. https://doi.org/10.1016/0020-7683(90)90004-f
- Suh J.B., Kelly S.G. Stress analysis of rubber block under vertical loading // J. Eng. Mech. 2012. V. 138. P. 770–783. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000390
- Mott P.H., Roland C.M. Uniaxial Deformation of Rubber Cylinders // Rubber Chem. Technol. 1995. V. 68. P. 739–745. https://doi.org/10.5254/1.3538770
- Horton J.M., Tupholme G.E., Gover M.J.C. Axial loading of bonded rubber blocks // J. Appl. Mech. 2002. V. 69. № 6. P. 836–843. https://doi.org/10.1115/1.1507769
- Qiao S., Lu N. Analytical solutions for bonded elastically compressible layers // Int. J. Solids Struct. 2015. V. 58. P. 353–365. https://doi.org/10.1016/j.ijsolstr.2014.11.018
- Timoshenko S. Theory of plates and shells. New York-Toronto-London: McGraw Hill Book Comp., 1959. = Timoshenko S.P. Elasticity theory course. Kuiv: Nauk. dumka. 1972. P. 507
- Uflyand Ya.S. Integral transforms in the problems of elasticity theory. ASUSSR, Moscow, Leningrad. 1963. P. 368 (in Russian).
- Lurie A.I. Spatial problems of elasticity theory. GITTL, Moscow. 1955. P. 491 (in Russian).
Қосымша файлдар
