title: The superposition method in the problem of bending of a thin isotropic plate clamped along the contour
metadata.name: dc.contributor.author
metadata.value: Alcybeev, Gleb O.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Goloskokov, Dmitriy P.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Matrosov, Alexander V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2023-01-19T19:47:03Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2023-01-19T19:47:03Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2022-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Alcybeev G. O., Goloskokov D. P., Matrosov A. V. The superposition method in the problem of bending of a thin isotropic plate clamped along the contour. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2022, vol. 18, iss. 3, pp. 347–364.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2022.305
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/38865
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In this work, the general solution of the differential equation for the bending of a thin isotropic plate under the action of a normal load applied to its plane is constructed by the superposition method. The solutions obtained by the method of initial functions in the form of trigonometric series are taken as two solutions, each of which allows satisfying the boundary conditions on two opposite sides of the plate. Two ways of satisfying the boundary conditions of a clamped plate are studied: the method of expansion into trigonometric Fourier series and the collocation method. It is shown that both methods give the same results and sufficiently fast convergence of the solution at all points of the plate except for small neighborhoods of the corner points. The constructed solution made it possible to study the behavior of the shear force in the corner points. Computational experiments have shown that when keeping 390 terms in the trigonometric series of the solution, the shear force is close to zero, but not identically equal.
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 18; Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: isotropic plate
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: bending of a thin plate
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: clamped plate
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: method of initial functions
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: MIF
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: computer algebra
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Maple
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: The superposition method in the problem of bending of a thin isotropic plate clamped along the contour
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 14519-Текст статьи-47925-1-10-20221010.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/38865/1/14519-%d0%a2%d0%b5%d0%ba%d1%81%d1%82%20%d1%81%d1%82%d0%b0%d1%82%d1%8c%d0%b8-47925-1-10-20221010.pdf
resources.format: Adobe PDF
resources.size: 499,05 kB