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Having taken curvilinear coordinates on the middle surface of shells in the lines of principle curvatures, we can determine the simplest system of 17 governing equations of the linear theory of shells. But sometimes, the problem of analytical determination of the equation of the middle surface in lines of principle curvatures is very difficult task and that is why it is necessary to use the system of 20 governing equations, derived by A.L. Goldenweiser for an arbitrary system of curvilinear coordinates with taking into account the condition of decomposition of the vectors of internal forces and moments and external surface load along the axes of the basic non-orthogonal moving trihedral. Later, the system of 20 governing equations, derived by the author, was published. These equations contain internal force factors and external surface load decomposed along the axes of the basic orthogonal moving trihedral. His paper shows that these both systems of governing equation can transform one into other with the help of the equations of translation, i.e. the both systems of governing equations are equivalent.

About the authors

S N Krivoshapko

RUDN University, Moscow, Russia

Author for correspondence.
117198, Москва, ул. Миклухо-Маклая, 6

д.т.н., профессор


  1. Goldenweiser, A.L. (1953). Theory of Elastic Thin Shells, Мoscow: GTTI. 544 p. (in Russian).
  2. Ivanov, V.N., Krivoshapko, S.N. (2010). Analytical Methods of Analysis of Shells of Complex Form: Monograph, Moscow: Izd-vo RUDN. 542 p. (in Russian).
  3. Rekach, V.G., Krivoshapko, S.N. (1977). On the problem of analysis of elastic thin shells given in non-orthogonal curvilinear coordinates. Raschet Obolochek Stroitel’nyh Konstruktziy: Sb. statey, Moscow: UDN. P. 3—14 (in Russian).
  4. Rynkovskaya, M.I. (2015). On the problem of strength analysis of thin ruled helical shells. Structural Mechanics of Engineering Constructions and Buildings. № 6. P. 13—15(in Russian).
  5. Bajoriya, G.Ch. (1985). An analysis of a long developable open helicoid with using of a moment theory in displacements. Stroitel’naya Mechanika i Raschet Soorujeniy. № 3. P. 22—24 (in Russian).
  6. Shevelev, L.P., Isaev, B.V. (1988). Non-linear equations of a theory of thin shells given in arbitrary coordinates, Zavod VTUZ pti PO turbostr. Leningrad. metal. z-da, 25 p., Dep. v VINITI 24.10.88. № 7604-В88 (in Russian).
  7. Konovalov, A.N. (1995). Numerical methods in static problems of theory of elasticity. Siberian Mathematical Journal. 36: 3. 491—505 (in Russian).
  8. Rimskiy, R.A. (1970). Issledovaniya Kosougol’nyh Plastin Metodom Kantorovicha – Vlasova. Issledovaniya po Teorii Soorujeniy. Moscow: Stroyizdat. 64—68 (in Russian).



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