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TsAGI Science Journal

ISSN Печать: 1948-2590
ISSN Онлайн: 1948-2604

TsAGI Science Journal

DOI: 10.1615/TsAGISciJ.2020033036
pages 673-678

THE SCHEME OF BIORTHOGONALIZATION OF VECTORS IN SOLVING THE PROBLEM OF RECTANGULAR PLATE BENDING

Vladimir Ivanovich Lysukhin
TUPOLEV, Academician Tupolev Embankment 17, Moscow, 105005, Russian Federation
Julian Fedotovich Yaremchuk
TUPOLEV, Academician Tupolev Embankment 17, Moscow, 105005, Russian Federation

Краткое описание

An approximate solution to the problem of bending a rectangular thin uniform plate under the application of a uniformly distributed load, the opposite sides of which are fixed and the other two sides are free, is considered. When solving this problem, a new computational scheme of solving the systems of linear algebraic equations is proposed. The procedure is based on constructing biorthogonal vectors in real vector space. As an intermediate result, a nondegenerate real matrix decomposition formula for the considered problem is obtained, which produces two triangular and diagonal matrices. It is demonstrated that for the considered example of computations, the proposed method is more accurate in comparison with the Gaussian method in relation to the main element choice.

ЛИТЕРАТУРА

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  2. Vainberg, D.V. and Vainberg, E.D., Computation of Plates, Kiev, Ukraine: Budivel'nik, 1970, (in Russian).

  3. Roknuzzaman, M., Hossain, M.B., Haque, M.R., and Ahmed, D.T.U., Analysis of Rectangular Plate with Opening by Finite Difference Method, Am. J. Civil Eng. Archit., vol. 3, no. 5, pp. 165-173, 2015.

  4. Amiryants, G.A., Vermel, V.D., Ishmuratov, F.Z., Kudryashov, A.B., Orlova, O.A., and Rudenko, D.S., Designing of Elastically Scaled Model of Aircraft Using Digital Technologies, TsAGI Sci. J., vol. 43, no. 3, pp. 381-398, 2012.

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  7. Voevodin, V.V., Computational Fundamentals of Linear Algebra, Moscow, Russia: Nauka, 1977.

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  10. Yaremchuk, Ju.F., Application of the Biorthogonalization Vectors Procedure to Applied Strength Problems, TsAGI Sci. J, vol. 48, no. 5, pp. 479-491, 2017.

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