Energy concerted the approach to research of elastic arbitrary shells

Аuthors

Firsanov V. V.^1*, Tran N. D.^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: ngocdoanmai@gmail.com

Abstract

In the framework of energy concerted course of the theory of shells an arbitrary shell is considered as a three - dimensional body. The state equations of such body are presented in the form of three-dimensional equations of elasticity theory in the thriorthogonal coordinate system. Principle of virtual work is applied for extracting two-dimensional equations and getting edge conditions. The components of deflected mode of a shell are expanded into polynomial series as functions of orthogonal coordinate. As an example cylindrical shell is considered. For practical analysis of such shell polynomials of quite low power are used. Such approach allows us to consider transverse tension and shear deformations and self-balanced components of edge forces. To solve the desired boundary problem the displacements are expanded into trigonometrical series depending on circumferential coordinate. The influence of shell thickness on components of the deflected mode is investigated. Comparison with the results of classical theory is given.

Keywords:

energy concerted theory, concerted conditions, three-dimensional equations of elasticity theory, elastic thin arbitrary shell, circular cylindrical shell, expansion of motions in series as functions of orthogonal coordinate, expansion in trigonometrical series, principle of virtual work, two-dimensional differential equations, edge conditions.