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This article is cited in 3 scientific papers (total in 3 papers)
Computer science
The superposition method in the problem of bending of a thin isotropic plate clamped along the contour
G. O. Alcybeeva, D. P. Goloskokovb, A. V. Matrosova a St Petersburg State University, 7-9, Universitetskaya nab., St Petersburg, 199034, Russian Federation
b St Petersburg Bonch-Bruevich State University of Telecommunications, 22, pr. Bol'shevikov, St Petersburg, 193232, Russian Federation
Abstract:
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.
Keywords:
isotropic plate, bending of a thin plate, clamped plate, method of initial functions, MIF, computer algebra, Maple.
Received: March 8, 2022 Accepted: June 21, 2022
Citation:
G. O. Alcybeev, D. P. Goloskokov, A. V. Matrosov, “The superposition method in the problem of bending of a thin isotropic plate clamped along the contour”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 18:3 (2022), 347–364
Linking options:
https://www.mathnet.ru/eng/vspui540 https://www.mathnet.ru/eng/vspui/v18/i3/p347
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