title: Mathematical modeling of bending of a thin orthotropic plate clamped along the contour
metadata.name: dc.contributor.author
metadata.value: Germider, Oksana V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Popov, Vasilii N.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2024-11-22T16:54:31Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2024-11-22T16:54:31Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2024-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Germider O. V., Popov V. N. Mathematical modeling of bending of a thin orthotropic plate clamped along the contour. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2024, vol. 20, iss. 3, pp. 310–323. https://doi.org/10.21638/spbu10.2024.301 (In Russian)
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu10.2024.301
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/47978
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Within the framework of Kirchhoff’s theory, a new approach to constructing a solution to
  the problem of modeling the bending of a thin rectangular orthotropic plate clamped along
  the contour, which is under the influence of a load normally distributed over its surface, is
  proposed. the solution to the inhomogeneous biharmonic equation for an orthotropic plate
  is obtained in the form of a partial sum of a double series in Chebyshev polynomials of
  the first kind. To find the coefficients in this expansion, the boundary value problem is
  reduced by the collocation method to a system of linear algebraic equations in matrix form
  using the properties of these polynomials. Based on matrix and differential transformations,
  expressions for bending moments and shearing forces are obtained. the results of calculations
  of the bending of the middle surface of the plate under different loads on the plate are
  presented, which demonstrate the effectiveness of the proposed approach.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This research was supported by the Russian Science Foundation, project N 24-21-00381,
  https://rscf.ru/project/24-21-00381/
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 20; Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: collocation method
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: biharmonic equation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Chebyshev polynomials of the first kind
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: bending of a thin orthotropic plate
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Mathematical modeling of bending of a thin orthotropic plate clamped along the contour
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: vestnik_spbu10_2024_310.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/47978/1/vestnik_spbu10_2024_310.pdf
resources.format: Adobe PDF
resources.size: 1,8 MB