title: The study of nonlinear deformation of a plane with an elliptical inclusion for harmonic materials
metadata.name: dc.contributor.author
metadata.value: Malkov, Venyamin M.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Malkova, Yulia V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2021-01-19T13:06:42Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2021-01-19T13:06:42Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Malkov V. M., Malkova Yu.V. The study of nonlinear deformation of a plane with an elliptical inclusion for harmonic materials. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2020, vol. 16, iss. 4, pp. 375–390.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2020.403
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/22453
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Analytical methods are used to study nonlinear deformation of a plane with an elliptical
  inclusion. The elastic properties of a material of the plane and inclusion are described with
  a semi-linear material. The external load is constant nominal (Piola) stresses at infinity. At
  the inclusion boundary, the conditions of the continuity for stresses and displacements are
  satisfied. Semi-linear material belongs to the class of harmonic, the methods of the theory of
  functions of a complex variable are applicable to solving nonlinear plane problems. Stresses and displacements are expressed in terms of two analytical functions of a complex variable,
  determined by the boundary conditions on the inclusion contour. It is assumed that the stress
  state of an inclusion is uniform (the tensor of nominal stresses is constant). This hypothesis
  made it possible to reduce the difficult nonlinear problem of conjugation of two elastic bodies
  to the solution of two more simpler problems for a plane with an elliptical hole. The validity
  of this hypothesis is justified by the fact that the constructed solution exactly satisfies all the
  equations and boundary conditions of the problem. The same hypothesis was used earlier by
  other authors to solve linear and nonlinear problems of an elliptical inclusion. In the article,
  a comparative analysis of the stresses and strains is carried out for two models of harmonic
  materials — semi-linear and John’s. Various variants of values of elasticity parameters of the
  inclusion and matrix have been considered.
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. Applied Mathematics. Computer Science. Control Processes;Volume 16; Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: nonlinear plane problem
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: elliptical inclusion
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: harmonic material
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: method of complex-variable functions
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: The study of nonlinear deformation of a plane with an elliptical inclusion for harmonic materials
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 375-390.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/22453/1/375-390.pdf
resources.format: Adobe PDF
resources.size: 397,63 kB