On the solution of the problem of axial compression of an elastic cylinder with specified ends displacement conditions

Мұқаба

Дәйексөз келтіру

Толық мәтін

Ашық рұқсат Ашық рұқсат
Рұқсат жабық Рұқсат берілді
Рұқсат жабық Тек жазылушылар үшін

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.

Толық мәтін

Рұқсат жабық

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

  1. 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
  2. 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
  3. 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
  4. Prokopov V.K. Axisymmetric problem of elasticity theory for an isotropic cylinder // Trudy LPI. 1950. № 2. P. 286–303 (in Russian).
  5. 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.
  6. 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
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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
  12. 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
  13. 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
  14. 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
  15. 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
  16. 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
  17. Uflyand Ya.S. Integral transforms in the problems of elasticity theory. ASUSSR, Moscow, Leningrad. 1963. P. 368 (in Russian).
  18. Lurie A.I. Spatial problems of elasticity theory. GITTL, Moscow. 1955. P. 491 (in Russian).

Қосымша файлдар

Қосымша файлдар
Әрекет
1. JATS XML
Жүктеу
2. Fig. 1. Calculation scheme of cylinder compression.

Жүктеу (103KB)
Метадеректер
3. Fig. 2. Finite element calculation model of cylinder compression.

Жүктеу (368KB)
Метадеректер
4. Fig. 3. Dependence of the maximum radial displacement of the lateral surface of the cylinder on the Poisson ratio and the form factor of the cylinder.

Жүктеу (278KB)
Метадеректер
5. Fig. 4. Distribution of stresses along the lateral surface of a cylinder under integral fulfillment of the conditions of absence of stresses on this surface: (a) – radial stress, (b) – tangential stress.

Жүктеу (95KB)
Метадеректер
6. Fig. 5. Approximation of residuals in radial and tangential stresses.

Жүктеу (95KB)
Метадеректер
7. Fig. 6. Dependence of the maximum radial displacement of the lateral surface of the cylinder on the Poisson ratio and the form factor of the cylinder after the 4th step.

Жүктеу (190KB)
Метадеректер

© Russian Academy of Sciences, 2025