Bending shell of revolution by transverse force and moment

Abstract

It is considered the bending of shell of revolution when the membrane resultants and stress couples of any cross section of shell are staticaly equivalent to title transverse force and title bending moment. Such kind of deformation and loading are called back-symmetric. Of the numerous works devoted to the study the stress- strain state of this kind should separate known monographs V. V. Novozhilov and K. F. Chernih, which make use of a complex transformation of the basic equations of the theory of shells and asymptotic method of their research and decisions. The material of the shell was assumed to be homogeneous isotropic and subjected to the Hook law. At that time, when there were no modern computing facilities, this approach has helped to solve many technical problems. In what follows the problem under consideration is reduced to the integration of the system of real ordinary differential equations of the first order, two of which are solved in quadratures. Unknown quantities of system coincide with boundary values. View of static boundary values is determined by the equations of equilibrium. The kinematic boundary values taken as generalized displacements corresponding to the generalized forces which are static boundary values. The basic system of differential equations will not change if we substitute the above given relations of the Hooke law other constitutive equations.

Keywords:

bending, transverse force, boundary values, compatibility conditions, stress-strain state