title: Bending of a clamped thin isotropic plate by the Kantorovich method using special polynomials
metadata.name: dc.contributor.author
metadata.value: Goloskokov, Dmitry P.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Matrosov, Alexander V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Olemskoy, Igor V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2024-02-19T13:19:02Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2024-02-19T13:19:02Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2023-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Goloskokov D. P., Matrosov A. V., Olemskoy I. V. Bending of a clamped thin isotropic plate by the Kantorovich method using special polynomials. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2023, vol. 19, iss. 4, pp. 423–442. https://doi.org/10.21638/11701/spbu10.2023.401 (In Russian)
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2023.401
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/44902
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The problem of bending a thin isotropic rectangular plate clamped on all four sides under
  the action of a normal load uniformly distributed over its surface is considered. An analytical
  solution of the boundary value problem for the resolving differential equation with respect
  to the normal deflection of the plate is obtained by the method of L. V. Kantorovich using
  special-type polynomials satisfying homogeneous boundary conditions. A feature of these
  polynomials is the so-called “quasi-orthogonality” property of the first and second derivatives,
  which leads to the splitting of the system of ordinary differential equations of the L. V. Kantorovich
  method into separate ordinary differential equations that are easily solved analytically.
  However, this property of polynomials is only approximately fulfilled. Two solutions are
  compared: an analytical one under the assumption of “quasi-orthogonality” of the first and
  second derivatives of polynomials and a numerical-analytical one without this assumption.
  The stress-strain state in the neighborhoods of corner points has been studied. It is shown
  that the moments and shear forces tend to zero when approaching the corners of the plate,
  as well as a double change in the sign of the shear force on the edge of the plate in the
  neighborhoods of the corner points.
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 19; Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: isotropic plate
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: bending of a thin isotropic plate
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: numerical-analytical methods
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: clamped plate
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: L. V. Kantorovich method
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: orthogonal polynomials
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Jacobi polynomials
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Bending of a clamped thin isotropic plate by the Kantorovich method using special polynomials
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 01.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/44902/1/01.pdf
resources.format: Adobe PDF
resources.size: 379,85 kB