The update theory calculation of the strain-stress state of cylindrical chells with variable thickness

Аuthors

Firsanov V. V.^1*, Doan T. N.^2**, Hieu L. T.^2***

1. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
2. Le Quy Don Technical University, 236, Hoang Quoc Viet, Ha Noi, Viet Nam

*e-mail: k906@mai.ru
**e-mail: trandoanmai@yandex.ru
***e-mail: lthieuhk@gmail.com

Abstract

The closed cylindrical shell with variable thickness being the function of longitudinal coordinate is considered as a three-dimensional body. The governing equations of three-dimensional elasticity theory are used. The components of strain- and stress state for the shell are represented as the polynomial functions of the thickness coordinate. These functions are two orders higher with respect to these of the Kirchhoff-Love theory. The virtual work principle is applied to obtainthe two-dimensional equations and its natural boundaryconditions.
At solving the boundary value problem for the closed shell the trigonometric expansions for the displacements with respect to the circumferential coordinate are used. The finite-difference method is used to solve the resulted ordinary differential equations with variable coefficients.
A circular cylindrical shell subjected to the uniformly distributed piecewise load is considered as an example. The effect of the shell thickness to its strain-stress state in boundary areas is analyzed. The transverse normal stress obtained by the proposed method and by the other variant of refined shell theory relation is compared to the classical shell theory. It is shown that the symmetrical change of the shell thickness has smallest effect to the stress distribution with respect to the normal coordinate.
Taking into account of the three-dimensional stress- strain state of the shell has shown that the transversal normal stress neglected in the classical theory may have order equal to the maximum bending stress one. This result allows one to estimate the strength and crack resistance of real shell structures.

Keywords:

circular cylindrical shell, three-dimensional equations of elasticity theory, variable thickness, components of the stress-strain state, virtual work principle, trigonometrits expansions, differential equations with variable coefficients, finite-difference method, boundary conditions, local loading, normal transverse stress

References

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