Geometric characteristics of the deformation state of the shells with orthogonal coordinate system of the middle surfaces

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Abstract


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.


About the authors

Vyacheslav N. Ivanov

Peoples’ Friendship University of Russia (RUDN University)

Author for correspondence.
Email: i.v.ivn@mail.ru
SPIN-code: 3110-9909
6 Miklukho-Maklaya St., Moscow, 117198, Russian Federation

Doctor of Technical Sciences, Professor, Department of Civil Engineering, Engineering Academy

Alisa A. Shmeleva

Peoples’ Friendship University of Russia (RUDN University)

Email: i.v.ivn@mail.ru
6 Miklukho-Maklaya St., Moscow, 117198, Russian Federation

graduate student of Department of Civil Engineering, Engineering Academy

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