On solving static contact problems for a semi-strip stamp on an anisotropic composite

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For the first time, the exact solution of the static contact problem of the frictionless action of a rigid die in the form of a semi-strip on an anisotropic multilayer composite material is constructed by the block element method. Previously, these important tasks in structural engineering practice, electronics, physics, and other fields were not solved. The difficulty in solving these contact problems with anisotropy, in comparison with the isotropic case, consists in the difficulty of describing the spectral properties of such mathematical objects as Green's functions and symbols of integral equations. Using existing numerical methods, it is possible to describe the behavior of the concentration of contact stresses at the stamp boundary in cases of isotropic materials. However, it was not possible to construct an accurate solution for the distribution of contact stresses in the anisotropic case under a semi-strip stamp, together with features at the boundary. For the first time, a solution was constructed reflecting the real distribution of contact stresses and their concentrations under the stamp. The solution obtained in the work tends to the solutions obtained for a strip or a quarter of the plane when the semi-strip degenerates into these areas.

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Sobre autores

V. Babeshko

Kuban State University; Southern Scientific Center of the Russian Academy of Sciences

Autor responsável pela correspondência
Email: babeshko41@mail.ru

Academician of the RAS

Rússia, Krasnodar; Rostov-on-Don

O. Evdokimova

Southern Scientific Center of the Russian Academy of Sciences

Email: babeshko41@mail.ru
Rússia, Rostov-on-Don

O. Babeshko

Kuban State University

Email: babeshko41@mail.ru
Rússia, Krasnodar

V. Evdokimov

Kuban State University

Email: babeshko41@mail.ru
Rússia, Krasnodar

Bibliografia

  1. Бабешко В.А., Евдокимова О.В., Бабешко О.М., Евдокимов В.С. К теории контактных задач для композитных сред с анизотропной структурой // Доклады РАН. Физика, технические науки. ДАН. 2024. Т. 518. С. 23–30.
  2. Горячева И.Г. Механика фрикционного взаимодействия М.: Наука, 2001. 478 с.
  3. Баженов В.Г., Игумнов Л.А. Методы граничных интегральных уравнений и граничных элементов. М.: Физматлит, 2008. 352 с.
  4. Калинчук В.В., Белянкова Т.И. Динамические контактные задачи для предварительно напряженных тел. М.: Физматлит, 2002. 240 с.
  5. Колесников В.И., Беляк О.А. Математические модели и экспериментальные исследования – основа конструирования гетерогенных антифрикционных материалов. М.: Физматлит, 2021. 265 с.
  6. Papangelo A., Ciavarella M., Barber J.R. Fracture Mechanics implications for apparent static friction coefficient in contact problems involving slip-weakening laws // Proc. Roy. Soc (London). 2015. A 471. Iss. 2180. Article Number 20150271.
  7. Ciavarella M. The generalized Cattaneo partial slip plane contact problem // Int. J. Solids Struct. I – Theory, II – Examples. 1998. V. 2349–2378.
  8. Zhou S., Gao X.L. Solutions of half-space and half-plane contact problems based on surface elasticity // Zeitschrift fr angewandte Mathematik und Physik. 2013. V. 64. P. 145–166.
  9. Guler M.A., Erdogan F. The frictional sliding contact problems of rigid parabolic and cylindrical stamps on graded coatings // Int. J. Mech. Sci. 2007. V. 49. P. 161–182.
  10. Ke L.-L., Wang Y.-S. Two-Dimensional Sliding Frictional Contact of Functionally Graded Materials // Eur. J. Mech. A. Solids. 2007. V. 26. P. 171–188.
  11. Almqvist A., Sahlin F., Larsson R., Glavatskih S. On the dry elasto-plastic contact of nominally flat surfaces // Tribology International. 2007. V. 40. № 4. P. 574–579.
  12. Almqvist A. An lcp solution of the linear elastic contact mechanics problem. 2013. http://www.mathworks.com/matlabcentral/fileexchange/43216
  13. Andersson L.E. Existence results for quasistatic contact problems with Coulomb friction // Appl. Math. Optim. 2000. V. 42. P. 169–202.
  14. Cocou M.A class of dynamic contact problems with Coulomb friction in viscoelasticity // Nonlinear Analysis: Real World Applications. 2015. V. 22. P. 508–519.
  15. Мангушев Р.А., Карлов В.Д., Сахаров И.И., Осокин А.И. Основания и фундаменты. М.: Изд-во АСВ, 2014. 392 с.
  16. Tsudik E. Analysis of structures in elastic foundations // Ross Publishing, 2013. 585 p.
  17. Айзикович С.М., Кудиш И.И. Приближенное аналитическое решение задачи о полосовом электроде на поверхности пьезоэлектроупругой полуплоскости с функционально-градиентным пьезоэлектроупругим покрытием // Проблемы прочности и пластичности. 2019. Т. 81. № 4. С. 393–401.
  18. Ворович И.И., Александров В.М., Бабешко В.А. Неклассические смешанные задачи теории упругости. М., 1974. 456 с.
  19. Бабешко В.А., Глушков Е.В., Зинченко Ж.Ф. Динамика неоднородных линейно-упругих сред. М.: Наука, 1989. 344 с.

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2. Fig. 1. The half-strip stamp extends to infinity only on the right.

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3. Fig. 2. Parameter γ of the singularity at the corner point of the stamp for different friction coefficients ε. For comparison with the result of the article, it is necessary to take ε = 0, θ/π = 0.25.

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