Geodesic
On the construction of solutions of the inhomogeneous biharmonic equation in problems of mechanics of thin isotropic plates
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 2, Tome 231 (2024), pp. 100-106

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In this paper, we propose a method for constructing a solution of the inhomogeneous biharmonic equation as applied to problems in the mechanics of thin isotropic plates. The method is based on the Chebyshev polynomial approximation of the eighth-order mixed partial derivative of the unknown function. Chebyshev polynomials of the first kind were used as basis functions. The proposed method is used to simulate the bending of an elastic isotropic rectangular plate under the action of a transverse load. The results obtained by the collocation method are analyzed; the roots of Chebyshev polynomials of the first kind are used as collocation points.
Mots-clés : polynomial approximation
Keywords: Chebyshev polynomials, rectangular plate, stress-strain state 
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     title = {On the construction of solutions of the inhomogeneous biharmonic equation in problems of mechanics of thin isotropic plates},
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V. N. Popov; O. V. Germider. On the construction of solutions of the inhomogeneous biharmonic equation in problems of mechanics of thin isotropic plates. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 2, Tome 231 (2024), pp. 100-106. http://geodesic.mathdoc.fr/item/INTO_2024_231_a9/