A stability of thin shells in view of the initial geometrical imperfections

Abstract

In the report the non-linear deformations and stability of thin shells are considered in view of initial geometrical imperfections. The energy balance low for shell deformation includes usually three components: strain energy depending on viscid and inviscid forces, work of external forces, kinetic energy. At quasistatic loading for steady branches it is possible to neglect components depending on viscous and dynamic forces. Frequently and the transient process is considered as static at which these components are neglected also, but in this case it is necessary to follow along a static curve of deformation, to select independent parameters of a solution as external load becomes unknown, and to search for methods of a detour of singular points. As a result the solution of a nonlinear problem of shell stability becomes very complicated. It is possible to go on "medium" path - to neglect the kinetic energy by leaving the component connected with viscid forces. This approach is a basis of a method of an additional viscosity (Yakushev [1-3]), which allows on a uniform algorithm to discover steady prebuckling and postbuckling states, to determine the upper and lower critical loads in view of initial geometrical imperfections and nonlinear properties of a material. Such approach gives a number of computing advantages, as the solution depends only on one parameter - time, there is no necessity to search for methods of the detour of singular points.