RAS Energy, Mechanics & ControlИзвестия Российской академии наук. Механика твердого тела Mechanics of Solids

  • ISSN (Print) 1026-3519
  • ISSN (Online) 3034-6428

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

PII
S30346428S1026351925020109-1
DOI
10.7868/S3034642825020109
Publication type
Article
Status
Published
Authors
Volume/ Edition
Volume / Issue number 2
Pages
179-195
Abstract
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.
Keywords
упругий цилиндр сжатие усреднение граничных условий приближенное решение
Date of publication
20.01.2026
Year of publication
2026
Number of purchasers
0
Views
13

References

  1. 1. Filon L.N.G. On the elastic equilibrium of circular cylinders under certain practical systems of load // Philos. Trans. R. Soc. Lond. 1901. V. 68. № 442–450. P. 147–233. https://doi.org/10.1098/rspl.1901.0056
  2. 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. 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. № 3. P. 176–182. https://doi.org/10.1115/1.4009381
  4. 4. Прокопов В.К. Осесимметричная задача теории упругости для изотропного цилиндра // Тр. ЛПИ. 1951. № 2. C. 286–303.
  5. 5. Валов Г.М. Об осесимметричной деформации сплошного кругового цилиндра конечной длины // ПММ. 1962. Т. 26. Вып. 4. C. 650–667.
  6. 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. № 2. P. 241–246. https://doi.org/10.1115/1.3564615
  7. 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/10.1023/A:1025066408575
  8. 8. Benthem J.P., Minderhoud P. The problem of the solid cylinder compressed between rough rigid stamps // Int. J. Solids Struct. 1972. V. 8. № 8. P. 1027–1042. https://doi.org/10.1016/0020-7683 (72)90067-4
  9. 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. № 40. P. 5707–5732. https://doi.org/10.1016/S0020-7683 (99)00289-9
  10. 10. Gent A.N., Lindley P.B. The compression of bonded rubber blocks // Proc. Inst. Mech. Eng. 1959. V. 173. № 1. P. 111–122. https://doi.org/10.1243/PIME_PROC_1959_173_022_02
  11. 11. Chalhoub M.S., Kelly J.M. Analysis of infinite-strip-shape base isolator with elastomer bulk compression // J. Eng. Mech. 1991. V. 117. № 8. P. 1791–1805. https://doi.org/10.1061/ (ASCE)0733-9399(1991)117:8(1791)
  12. 12. Suh J.B., Kelly S.G. Stress analysis of rubber block under vertical loading // J. Eng. Mech. 2012. V. 138. P. 770–783.
  13. 13. Mott P.H., Roland C.M. Uniaxial deformation of rubber cylinders // Rubber Chem. Technol. 1995. V. 68. № 5. P. 739–745. https://doi.org/10.5254/1.3538770
  14. 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. 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. 16. Timoshenko S. Theory of plates and shells. New York-Toronto-London: McGraw Hill Book Comp., 1959. = Тимошенко C.П. Курс теории упругости. Киев: Наук. Думка, 1972. 507 c.
  17. 17. Уфлянд Я.С. Интегральные преобразования в задачах теории упругости. М.Л.: Изд. АН СССР, 1963. 368 с.
  18. 18. Лурье А.И. Пространственные задачи теории упругости. М.: Гостехиздат, 1955. 491 с.
QR
Translate

Индексирование

Scopus

Scopus

Scopus

Crossref

Scopus

Higher Attestation Commission

At the Ministry of Education and Science of the Russian Federation

Scopus

Scientific Electronic Library