title: On contact problems with a deformable punch and variable rheology
metadata.name: dc.contributor.author
metadata.value: Babeshko, Vladimir A.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Evdokimova, Olga V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Babeshko, Olga M.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Zaretskaya, Marina V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Evdokimov, Vladimir S.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2023-12-26T16:12:50Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2023-12-26T16:12:50Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2023-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Babeshko V.A., Evdokimova O.V., Babeshko O. M., Zaretskaya M.V., Evdokimov V. S. On contact problems with a deformable punch and variable rheology. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2023, vol. 10 (68), issue 4, pp. 588– 599. https://doi.org/10.21638/spbu01.2023.401 (In Russian)
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2023.401
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/44549
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The paper presents for the first time one of the methods for studying and solving contact
  problems with a deformed stamp for those cases when there is a need to change the rheology
  of the stamp material. It is based on a new universal modeling method previously
  published by the authors, which is used in boundary value problems for systems of partial
  differential equations. With its help, solutions of complex vector boundary value problems
  for systems of differential equations can be decomposed into solutions of scalar boundary
  value problems for individual differential equations. Among them, the Helmholtz equations
  are the simplest. Solutions to scalar boundary value problems are represented as fractals,
  self-similar mathematical objects, first introduced by the American mathematician B. Mandelbrot.
  The role of fractals is performed by packed block elements. The transition from
  systems of differential equations in partial derivatives to individual equations is carried
  out using the transformation of academician B. G. Galerkin or representation by potentials.
  It is known that the solutions of dynamic contact problems with a deformable stamp
  of complex rheology are cumbersome and their study is always difficult. The problem is
  complicated by the presence of discrete resonant frequencies in such problems, which were
  once discovered by Academician I. I. Vorovich. A contact problem with a deformable punch
  admits the construction of a solution if it is possible to solve the contact problem for an
  absolutely rigid punch and construct a solution to the boundary problem for a deformable
  punch. In earlier works of the authors, the deformable stamp was described by a separate
  Helmholtz equation. In this paper, we consider a contact problem on the action of a semiinfinite
  stamp on a multilayer base, described by the system of Lame equations. One of
  the methods of transition to other rheologies is shown when describing the properties of a
  deformable stamp in contact problems.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The work was supported by the Russian Science Foundation (project 22-21-00129).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 10(68); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: block element
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: factorization
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: integral equations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: external forms
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: cracks of a new type
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On contact problems with a deformable punch and variable rheology
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 588-599.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/44549/1/588-599.pdf
resources.format: Adobe PDF
resources.size: 310,17 kB