Learning of contact problems on the effect of an acute-angled wedge-shaped stamp on an anisotropic composite

Authors

UDC

539.3

EDN

HIKYJA

DOI:

10.31429/vestnik-23-1-30-36

Abstract

For the first time, an accurate solution of contact problems on the effect of acute-angled wedge-shaped stampson an anisotropic composite multilayer medium is constructed. The block element method is used in combination with topological and factorization approaches, which made it possible to overcome the problem of solving contact problems in a two-dimensional wedge-shaped domain. This result is achieved by first constructing an exact solution of the two-dimensional Wiener–Hopf integral equation, followed by constructing wedge-shaped carrier homeomorphisms. The constructed solution opened up the possibility not only to study the structural properties of multicomponent anisotropic composites in contact with dies of the specified shape, but also to study the strength and fracture of block structures of different sized blocks and inclusions that occur in seismology. In addition, the solution of this problem has opened up the possibility of creating a new type of surface wave emitters and transducers not previously described for wedge-shaped regions, which may be useful in problems of electronics, acoustics and nanomaterials.

Keywords:

contact problems, wedge-shaped, acute-angled stamp, anisotropic composite, factorization

Funding information

This work was supported by the Russian Science Foundation and the Kuban Science Foundation, regional project no. 24-11-20006.

Author info

  • Vladimir S. Evdokimov

    аспирант кафедры математического моделирования Кубанского государственного университета

References

  1. Freund, L.B., Dynamic Fracture Mechanics. Cambridge, UK, Cambridge University Press, 1998.
  2. Achenbach, J.D., Wave propagation in Elastic Solids. North-Holland Series in Applied Mathematics and Mechanics. Amsterdam, North-Holland, 1973.
  3. Abrahams, I.D., Wickham, G.R. General Wiener-Hopf factorization matrix kernels with exponential phase factors. Journal of Applied Mathematics, 1990, vol. 50, pp. 819–838.
  4. Norris, A.N., Achenbach, J.D., Elastic wave diffraction by a semi infinite crack in a transversely isotropic material. Journal of Applied Mathematics and Mechanics, 1984, vol. 37, pp. 565–580.
  5. Нобл, Б., Метод Винера–Хопфа. Москва, Иностранная литература, 1962. [Noble, B., Metod Vinera–Khopfa = The Wiener-Hopf Method. Moscow, Foreign Literature, 1962. (in Russian)]
  6. Ткачева, Л.А., Плоская задача о колебаниях плавающей упругой пластины под действием периодической внешней нагрузки. Прикладная механика и техническая физика, 2004, т. 45, № 5 (273), с. 136–145. [Tkacheva, L.A., A plane problem of oscillations of a floating elastic plate under the action of a periodic external load. Prikladnaya mekhanika i tekhnicheskaya fizika = Applied Mechanics and Technical Physics, 2004, vol. 45, no. 5 (273), pp. 136–145. (in Russian)]
  7. Chakrabarti, A., George, A.J., Solution of a singular integral equation involving two intervals arising in the theory of water waves. Applied Mathematics Letters, 1994, vol. 7, pp. 43–47.
  8. Davis, A.M.J., Continental shelf wave scattering by a semi-infinite coastline. Geophysics, Astrophysics, Fluid Dynamics, 1987, vol. 39, pp. 25–55.
  9. Горячева, И.Г., Механика фрикционного взаимодействия. Москва, Наука, 2001. [Goryacheva, I.G., Mekhanika friktsionnogo vzaimodeystviya = Mechanics of Frictional Interaction. Moscow, Nauka, 2001. (in Russian)]
  10. Горячева, И.Г., Мещерякова, А.Р., Моделирование накопления контактно-усталостных повреждений и изнашивания в контакте неидеально гладких поверхностей. Физическая мезомеханика, 2022, т. 25, № 4, c. 44–53. [Goryacheva, I.G., Meshcheryakova, A.R., Modeling the accumulation of contact fatigue damage and wear in the contact of imperfectly smooth surfaces. Fizicheskaya mezomekhanika = Physical Mesomechanics, 2022, vol. 25, no. 4, pp. 44–53. (in Russian)]
  11. Баженов, В.Г., Игумнов, Л.А., Методы граничных интегральных уравнений и граничных элементов. Москва, Физматлит, 2008. [Bazhenov, V.G., Igumnov, L.A., Metody granichnykh integral'nykh uravneniy i granichnykh elementov = Methods of boundary integral equations and boundary elements. Moscow, Fizmatlit, 2008. (in Russian)]
  12. Калинчук, В.В., Белянкова, Т.И., Динамика поверхности неоднородных сред. Москва, Физматлит, 2009. [Kalinchuk, V.V., Belyankova, T.I., Dinamika poverkhnosti neodnorodnykh sred = Dynamics of the surface of inhomogeneous media. Moscow, Fizmatlit, 2009. (in Russian)]
  13. Калинчук, В.В., Белянкова, Т.И., Динамические контактные задачи для предварительно напряженных тел. Москва, Физматлит, 2002. [Kalinchuk, V.V., Belyankova, T.I., Dinamicheskie kontaktnye zadachi dlya predvaritel'no napryazhennykh tel = Dynamic contact problems for prestressed bodies. Moscow, Fizmatlit, 2002. (in Russian)]
  14. Ворович, И.И., Бабешко, В.А., Динамические смешанные задачи теории упругости для неклассических областей. Москва, Наука, 1979. [Vorovich, I.I., Babeshko, V.A., Dinamicheskie smeshannye zadachi teorii uprugosti dlya neklassicheskikh oblastey = Dynamic mixed problems of elasticity theory for non-classical domains. Moscow, Nauka, 1979. (in Russian)]
  15. Ватульян, А.О., Контактные задачи со сцеплением для анизотропного слоя. Прикладная математика и механика, 1977, т. 41, № 4, с. 727–734. [Vatulyan, A.O., Contact problems with adhesion for an anisotropic layer. Prikladnaya matematika i mekhanika = Applied Mathematics and Mechanics, 1977, vol. 41, no. 4, pp. 727–734. (in Russian)]
  16. Колесников, В.И., Беляк, О.А., Математические модели и экспериментальные исследования –- основа конструирования гетерогенных антифрикционных материалов. Москва, Физматлит, 2021. [Kolesnikov, V.I., Belyak, O.A., Matematicheskie modeli i eksperimental'nye issledovaniya –- osnova konstruirovaniya geterogennykh antifriktsionnykh materialov = Mathematical models and experimental studies –- the basis for the design of heterogeneous antifriction materials. Moscow, Fizmatlit, 2021. (in Russian)]
  17. Бабешко, В.А., Глушков, Е.В., Зинченко, Ж.Ф., Динамика неоднородных линейно-упругих сред. Москва, Наука, 1989. [Babeshko, V.A., Glushkov, E.V., Zinchenko, Zh.F., Dinamika neodnorodnykh lineyno-uprugikh sred = Dynamics of inhomogeneous linear-elastic media. Moscow, Nauka, 1989. (in Russian)]
  18. Кристенсен, Р., Введение в механику композитов. Москва, Мир, 1982. [Christensen, R., Vvedenie v mekhaniku kompozitov = Introduction to Composite Mechanics. Moscow, Mir, 1982. (in Russian)]
  19. Kushch, V.I., Micromechanics of composites: multipole expansion approach. Oxford, Waltham, Elsevier Butterworth-Heinemann, 2013.
  20. McLaughlin, R., A study of the differential scheme for composite materials. International Journal of Engineering Science, 1977, vol. 15, pp. 237–244.
  21. Бабешко, В.А., Евдокимова, О.В., Бабешко, О.М., Евдокимов, В.С., Точное решение двумерного интегрального уравнения Винера-Хопфа в смешанных задачах анизотропных сред. Прикладная механика и теоретическая физика, 2025. [Babeshko, V.A., Evdokimova, O.V., Babeshko, O.M., Evdokimov, V.S., Exact solution of the two-dimensional Wiener-Hopf integral equation in mixed problems of anisotropic media. Prikladnaya mekhanika i teoreticheskaya fizika = Applied Mechanics and Theoretical Physics, 2025. (in Russian)] DOI: 10.15372/PMTF202515650
  22. Бабешко, В.А., Евдокимова, О.В., Бабешко, О.М., Точное решение универсальным методом моделирования контактной задачи в четверти плоскости многослойной среды. Прикладная математика и механика, 2022, т. 86, № 5, с. 628–637. [Babeshko, V.A., Evdokimova, O.V., Babeshko, O.M., Exact solution by a universal method for modeling a contact problem in a quarter plane of a multilayer medium. Prikladnaya matematika i mekhanika = Applied Mathematics and Mechanics, 2022, vol. 86, no. 5, pp. 628–637. (in Russian)] DOI: 10.31857/S0032823522050046

Downloads

Download data is not yet available.

Downloads

Issue

Vol. 23 (2026) No. 1

Pages

30-36

Section

Mechanics

Dates

Submitted

January 26, 2026

Accepted

March 17, 2026

Published

March 24, 2026

How to Cite

[1]
Evdokimov, V.S., Learning of contact problems on the effect of an acute-angled wedge-shaped stamp on an anisotropic composite. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2026, т. 23, № 1, pp. 30–36. DOI: 10.31429/vestnik-23-1-30-36

License

Copyright (c) 2026 Евдокимов В.С.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Similar Articles

1-10 of 1102

You may also start an advanced similarity search for this article.

Most read articles by the same author(s)

1 2 > >>