Approximate Analytical Solutions in the Analysis of Thin Elastic Plates

A.V. Matrosov, Dmitriy P. Goloskokov

Research output

Abstract

Two approaches to the construction of approximate analytical solutions for bending of a rectangular thin plate are presented: the superposition method based on the method of initial functions (MIF) and the one built using the Green's function in the form of orthogonal series. Comparison of two approaches is carried out by analyzing a square plate clamped along its contour. Behavior of the moment and the shear force in the neighborhood of the corner points is discussed. It is shown that both solutions give identical results at all points of the plate except for the neighborhoods of the corner points. There are differences in the values of bending moments and generalized shearing forces in the neighborhoods of the corner points.

Original languageEnglish
Title of host publicationEIGHTH POLYAKHOV'S READING
EditorsE Kustova, G Leonov, N Morosov, M Yushkov, M Mekhonoshina
PublisherAmerican Institute of Physics
Number of pages7
DOIs
Publication statusPublished - 2018
EventВосьмые Поляховские чтения: международная научная конференция по механике - Старый Петергоф, Saint Petersburg
Duration: 29 Jan 20182 Feb 2018
Conference number: 8
https://events.spbu.ru/events/polyakhov_readings
http://nanomat.spbu.ru/en/node/175
http://nanomat.spbu.ru/ru/node/192
http://spbu.ru/news-events/calendar/viii-polyahovskie-chteniya

Publication series

NameAIP Conference Proceedings
PublisherAMER INST PHYSICS
Volume1959
ISSN (Print)0094-243X

Conference

ConferenceInternational Scientific Conference on Mechanics - Eighth Polyakhov's Reading
CountryRussian Federation
CitySaint Petersburg
Period29/01/182/02/18
Internet address

Cite this

Matrosov, A. V., & Goloskokov, D. P. (2018). Approximate Analytical Solutions in the Analysis of Thin Elastic Plates. In E. Kustova, G. Leonov, N. Morosov, M. Yushkov, & M. Mekhonoshina (Eds.), EIGHTH POLYAKHOV'S READING (AIP Conference Proceedings; Vol. 1959). American Institute of Physics. https://doi.org/10.1063/1.5034687
Matrosov, A.V. ; Goloskokov, Dmitriy P. / Approximate Analytical Solutions in the Analysis of Thin Elastic Plates. EIGHTH POLYAKHOV'S READING. editor / E Kustova ; G Leonov ; N Morosov ; M Yushkov ; M Mekhonoshina. American Institute of Physics, 2018. (AIP Conference Proceedings).
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abstract = "Two approaches to the construction of approximate analytical solutions for bending of a rectangular thin plate are presented: the superposition method based on the method of initial functions (MIF) and the one built using the Green's function in the form of orthogonal series. Comparison of two approaches is carried out by analyzing a square plate clamped along its contour. Behavior of the moment and the shear force in the neighborhood of the corner points is discussed. It is shown that both solutions give identical results at all points of the plate except for the neighborhoods of the corner points. There are differences in the values of bending moments and generalized shearing forces in the neighborhoods of the corner points.",
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Matrosov, AV & Goloskokov, DP 2018, Approximate Analytical Solutions in the Analysis of Thin Elastic Plates. in E Kustova, G Leonov, N Morosov, M Yushkov & M Mekhonoshina (eds), EIGHTH POLYAKHOV'S READING. AIP Conference Proceedings, vol. 1959, American Institute of Physics, Saint Petersburg, 29/01/18. https://doi.org/10.1063/1.5034687

Approximate Analytical Solutions in the Analysis of Thin Elastic Plates. / Matrosov, A.V.; Goloskokov, Dmitriy P.

EIGHTH POLYAKHOV'S READING. ed. / E Kustova; G Leonov; N Morosov; M Yushkov; M Mekhonoshina. American Institute of Physics, 2018. (AIP Conference Proceedings; Vol. 1959).

Research output

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T1 - Approximate Analytical Solutions in the Analysis of Thin Elastic Plates

AU - Matrosov, A.V.

AU - Goloskokov, Dmitriy P.

PY - 2018

Y1 - 2018

N2 - Two approaches to the construction of approximate analytical solutions for bending of a rectangular thin plate are presented: the superposition method based on the method of initial functions (MIF) and the one built using the Green's function in the form of orthogonal series. Comparison of two approaches is carried out by analyzing a square plate clamped along its contour. Behavior of the moment and the shear force in the neighborhood of the corner points is discussed. It is shown that both solutions give identical results at all points of the plate except for the neighborhoods of the corner points. There are differences in the values of bending moments and generalized shearing forces in the neighborhoods of the corner points.

AB - Two approaches to the construction of approximate analytical solutions for bending of a rectangular thin plate are presented: the superposition method based on the method of initial functions (MIF) and the one built using the Green's function in the form of orthogonal series. Comparison of two approaches is carried out by analyzing a square plate clamped along its contour. Behavior of the moment and the shear force in the neighborhood of the corner points is discussed. It is shown that both solutions give identical results at all points of the plate except for the neighborhoods of the corner points. There are differences in the values of bending moments and generalized shearing forces in the neighborhoods of the corner points.

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BT - EIGHTH POLYAKHOV'S READING

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PB - American Institute of Physics

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Matrosov AV, Goloskokov DP. Approximate Analytical Solutions in the Analysis of Thin Elastic Plates. In Kustova E, Leonov G, Morosov N, Yushkov M, Mekhonoshina M, editors, EIGHTH POLYAKHOV'S READING. American Institute of Physics. 2018. (AIP Conference Proceedings). https://doi.org/10.1063/1.5034687