Structural Mechanics of Engineering Constructions and BuildingsStructural Mechanics of Engineering Constructions and Buildings1815-52352587-8700Peoples’ Friendship University of Russia (RUDN University)2300810.22363/1815-5235-2020-16-1-38-44Research ArticleGeometric characteristics of the deformation state of the shells with orthogonal coordinate system of the middle surfacesIvanovVyacheslav N.<p>Doctor of Technical Sciences, Professor, Department of Civil Engineering, Engineering Academy</p>i.v.ivn@mail.ruShmelevaAlisa A.<p>graduate student of Department of Civil Engineering, Engineering Academy</p>i.v.ivn@mail.ruPeoples’ Friendship University of Russia (RUDN University)15122020161384427022020Copyright © 2020, Ivanov V.N., Shmeleva A.A.2020<p>The aim of this work is to receive the geometrical equations of strains of shells at the common orthogonal not conjugated coordinate system. At the most articles, textbooks and monographs on the theory and analysis of the thin shell there are considered the shells the coordinate system of which is given at the lines of main curvatures. Derivation of the geometric equations of the deformed state of the thin shells in the lines of main curvatures is given, specifically, at monographs of the theory of the thin shells of V.V. Novozhilov, K.F. Chernih, A.P. Filin and other Russian and foreign scientists. The standard methods of mathematic analyses, vector analysis and differential geometry are used to receive them. The method of tensor analysis is used for receiving the common equations of deformation of non orthogonal coordinate system of the middle shell surface of thin shell. The equations of deformation of the shells in common orthogonal coordinate system (not in the lines of main curvatures) are received on the base of this equation. Derivation of the geometric equations of deformations of thin shells in orthogonal not conjugated coordinate system on the base of differential geometry and vector analysis (without using of tensor analysis) is given at the article. This access may be used at textbooks as far as at most technical institutes the base of tensor analysis is not given.</p>theory of thin shellsgeometric equationsdeformationsvector analysisтеория тонких оболочекгеометрические уравнениядеформациивекторный анализ[Aron H. Das Gleichgewlcht und die Bewegund einer unendlich dunnen beliebig gekrummten elastischen Schale. J. fur reine und angew, Math. 1874;78:136–174.][Love A. The small free vibrations and deformation of thin elastic shell. Pfill. Transs Roy. Soc. 1888;179(A): 491–546.][Vlasov V.Z. Obshchaya teoriya obolochek i ee prilozheniya v tekhnike [General theory of shells and its application at technology]. Moscow; Leningrad: Gostehizdat Publ.; 1949. (In Russ.)][Novozhilov V.V. 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