Contact problem of elastic strips with initial stresses with periodically placed resilient protective strap

Authors

  • N.N. Dikhtyaruk Khmelnitsky National University, Ukraine
  • O.V. Kurinienko Khmelnitsky National University, Ukraine
  • E.A. Poplavskaya Khmelnitsky National University, Ukraine

DOI:

https://doi.org/10.31891/2079-1372-2019-92-2-6-12

Keywords:

linearized theory of elasticity, initial (residual) stress, contact problems, Fourier integral transformations.

Abstract

The present article considers the formulation and solution of the problem on contact interaction of a pre-stressed band with regularly placed  elastic cover plates. The study has been carried out within the framework of the linearized elasticity theory in general form for the theory of large (finite) initial deformations and two variants of the theory of small initial deformations with an arbitrary structure of the elastic potential [1]. The solution of the problem comes down to a singular integro-differential equation for unknown contact stresses with a kernel expressed in the form of a sum of the kernel and some regular kernel under certain boundary conditions. The solution sought is given in the form of a series of Jacobi polynomials. A quasiregular infinite system of linear equations is obtained in order to determine the unknown coefficients of the series [2].

References

1. Guz A.N. Kontaktnoe vzaimodejstvie uprugih tel s nachalnymi (ostatochnymi) napryazheniyami / A.N. Guz, S.Yu. Babich, V.B. Rudnickij // Razvitie idej L.A. Galina v mehanike. K stoletiyu so dnya rozhdeniya uchenogo. – M. ; Izhevsk : In-t komp’yuter. issled., 2013. – S. 188–244.
2. Guz A.N. Osnovy teorii kontaktnogo vzaimodejstviya uprugih tel s nachalnymi (ostatochny-mi) napryazheniyami [Tekst] / A.N. Guz, V.B. Rudnickij. – Hmelnickij: Izd-vo “PP Melnik”, 2006. – 710 s.
3. Dihtyaruk N.N. O ravnovesii polosy s nachalnymi napryazheniyami, usilennoj uprugimi na-kladkami / N.N. Dihtyaruk // Prikl. mehanika. – 2004, – 40, № 3 – S. 63–70.
4. Dihtyaruk M. M. Peredacha navantazhennya vid neskinchennogo stringera do dvoh zatisnenih po odnomu krayu odnakovih smug z pochatkovimi (zalishkovimi) napruzhennyami / M. M. Dihtyaruk // Visnik TNTU. – 2016, – 83, № 3, – S. 51–60.
5. E. Melan, “Ein Beitrag zur Theorie geschweiss der Verbindungen,“ Ingenieur Archiv, 3, No. 2, 126–128.
6. Rudnickij, V. B., Dihtyaruk N.N. Uprugaya polosa s nachalnymi napryazheniyami, usilennaya up-rugimi nakladkami./ V. B. Rudnickij, N.N. Dihtyaruk // Prikl. mehanika, 2002, – 38, № 11, – S. 81–88.
7. Rudnickij, V. B., Dihtyaruk N.N. Kontaktnaya zadacha o vzaimodejstvii beskonechnogo stringera i dvuh odinakovyh polos s nachalnymi napryazheniyami. / V.B. Rudnickij, N.N. Dihtyaruk // Prikl. meha-nika., 2017, – 53, № 2, – S. 41–48.
8. Dikhtyaruk, N.N. Equilibrium of a prestressed strip reinforced with elastic plates // International Ap-plied Mechanics. – March 2004, Volume 40, Issue 3, pp 290–296.
9. Rudnitskii V.B , Dikhtyaruk N.N. A prestressed elastic strip with elastic reinforcements / V.B. Rud-nitskii, N.N. Dikhtyaruk// International Applied Mechanics. – November 2002, Volume 38, Issue 11, pp. 1354–1360.
10. Rudnitskii V.B., Dikhtyaruk N.N. Interaction Between an Infinite Stringer and Two Identical Prestressed Strips: Contact Problem /, V.B. Rudnitskii, N.N Dikhtyaruk // Translated from Prikladnaya Mek-hanika, Vol. 53, No. 2, pp. 41–48, March–April, 2017. 11. Dihtyaruk M.M. Pidsilena pruzhna smuga z pochatkovimi napruzhennyami pid diyeyu vertikalnoyi sili [Tekst] / M.M. Dihtyaruk, O.V. Kurinyenko
11. Dihtyaruk M.M. Pidsilena pruzhna smuga z pochatkovimi napruzhennyami pid diyeyu vertikalnoyi sili [Tekst] / M.M. Dihtyaruk, O.V. Kurinyenko // Problemi tribologiyi. – 2018. – №2. – S. 29–34.

Downloads

Published

2019-07-26

How to Cite

Dikhtyaruk, N., Kurinienko, O., & Poplavskaya, E. (2019). Contact problem of elastic strips with initial stresses with periodically placed resilient protective strap. Problems of Tribology, 24(2/92), 6–12. https://doi.org/10.31891/2079-1372-2019-92-2-6-12

Issue

Section

Articles