Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Deformation of thin-walled rings under the action of n concentrated and distributed forces


Equations for displacement of the elastic line of the cross-section of a ring under the action of n lumped forces with allowance for radial displacements due to bending and compression (tension) and to n forces applied over arcs are derived. The maximum displacement values and the associated shape deviations and possibilities of their reduction are presented. Application of the obtained results in design and in technological calculations is illustrated by examples.

This is a preview of subscription content, log in to check access.


  1. 1.

    Timoshenko SP (1955) Strength of materials (in English). 3rd edn., New York: Van Nostrand Co., Inc. Princeton, N.J., pt I, XIV + 442p., pt II, 1956, XVI + 572p

  2. 2.

    Boyarshinov SV (1983) Fundamentals of machine construction mechanics (university textbook; in Russian). Mashinostroenie, Moscow, pp 120–137

  3. 3.

    Ponomarev SD, Biderman VL et al (1950) Fundamentals of current strength calculation methods in machine construction. Moscow, Mashgiz (in Russian)

  4. 4.

    Korsakov VS (1961) Precision in machining (in Russian). Mashgiz: Moscow. pp 166-174

  5. 5.

    (1968) Strength, stability vibration (in Russian). Handbook, pt I, I.A. Birger and Y.G. Panovko, editors, Moscow: Mashinostroenie, pp. 321, 631

  6. 6.

    Lopatukhin I, Talybov R, Ber A (2000) Improvement of thin-walled cylindrical workpiece machining accuracy by means of control programs. Int J Manuf Sci Prod 3(1):7–11 in English

  7. 7.

    Lopatukhin IM (1981) Deformation of thin-walled rings under the action of n forces. Raschet i proektirovanie mekhanicheskikh sistem. AzPI. 213-219

  8. 8.

    Lopatukhin IM (1985) Deformation of thin-walled rings. Izvestiya Vuzov, Mashinostroenie, No. 2, pp 10-14. The Engineering Index Annual 1985, No 095880 p. 7626 (in English)

  9. 9.

    Lopatukhin IM, Sutovskii DM (1977) Study of influence of structure of gripping surfaces on deformation (macrogeometry) under fixing of thin-walled workpieces. Izvestiya Vuzov, Mashinostroenie, (Izv. Vyssh. Uchebn. Zaved., Mashinostr.), No. 7, pp 152-155

  10. 10.

    Lopatukhin I (2006) Fundamentals of machine construction technology. Part II. Mikhlol Publishing House Ltd., Code 11030135 in Hebrew (pp. 151-159) and Code 11030141 in Russian (pp. 159-167), Technion-Israel Institute of Technology, Haifa, ISRAEL

Download references

Author information

Correspondence to Isak Lopatukhin.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Lopatukhin, I., Khaskel’berg, L. Deformation of thin-walled rings under the action of n concentrated and distributed forces. Int J Adv Manuf Technol 49, 627–634 (2010).

Download citation


  • Ring
  • n forces
  • Displacements
  • Shape deviations