Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya
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Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya, 2021, Volume 17, Issue 2, Pages 120–130
DOI: https://doi.org/10.21638/11701/spbu10.2021.202
(Mi vspui483)
 

This article is cited in 1 scientific paper (total in 1 paper)

Applied mathematics

Bending of a ribbed plate under complex loading

D. P. Goloskokova, A. V. Matrosovb

a The Bonch-Bruevich St. Petersburg State University of Telecommunication, 22, pr. Bol'shevikov, St. Petersburg, 193232, Russian Federation
b St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
Full-text PDF (479 kB) Citations (1)
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Abstract: The article considers the problem of a rectangular plate, supported by a cross system of stiffening ribs, bending. In addition to the transverse load, the plate is subjected to forces in its plane, transmitted through the ribs. An analytical solution to the boundary value problem for the resolving differential equation with respect to the normal deflection of the plate, describing the deformation of a rectangular plate supported by stiffeners, is obtained. The solution is presented in the form of series in combinations of regular and special discontinuous functions, which converge quickly and lead to a simple computational algorithm. The influence of the ribs is taken into account in the equation in the form of additional terms containing factors with a delta function. This approach allows us to get rid of a number of assumptions regarding the interaction of the plate with its reinforcing elements. The use of the apparatus of generalized functions when modeling objects of this type simplifies the boundary conditions (there are no conditions for conjugation of various structural elements), but at the same time the differential equations become more complicated. The problem is reduced to the so-called partially degenerate equations. Development of analytical methods that allow obtaining exact solutions of differential equations of this type, and their introduction into computational practice, is one of the urgent tasks of the mechanics of objects with disturbed regularity.
Keywords: plate, stiffeners, mathematical model, numerical-analytical methods, special discontinuous functions, Dirac function, Heaviside function, Fourier series, orthogonal series.
Received: February 4, 2021
Accepted: April 5, 2021
Document Type: Article
UDC: 539.3
MSC: 35C10, 74E10, 74B05
Language: Russian
Citation: D. P. Goloskokov, A. V. Matrosov, “Bending of a ribbed plate under complex loading”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 17:2 (2021), 120–130
Citation in format AMSBIB
\Bibitem{GolMat21}
\by D.~P.~Goloskokov, A.~V.~Matrosov
\paper Bending of a ribbed plate under complex loading
\jour Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr.
\yr 2021
\vol 17
\issue 2
\pages 120--130
\mathnet{http://mi.mathnet.ru/vspui483}
\crossref{https://doi.org/10.21638/11701/spbu10.2021.202}
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Вестник Санкт-Петербургского университета. Серия 10. Прикладная математика. Информатика. Процессы управления
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    Full-text PDF :16
    References:23
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