About the global picture of stability of equilibrium states of geometrically nonlinear deformable systems

Abstract

Despite the long history of t he theory of stability of deformable system, many basic notions, statements and theorems are applied, unfortunately, not rarely incorrectly. This situation is a result of the fineness, complexity, and diversity of the phenomena conllected with diverse aspects of the loss of stability of equilibrium states of nonlinear deformable systems. The first part of the article is devoted to the attempt of elucidation of the use of a number of basic statements as the exchange of stabilities at singular points, or the effect of disappearance of bifurcation phenomena as result of geometrical imperfection of the system, and others. The second part of the present work deals with the method of investigation of the global picture of stability of nonlinear deformable systems subjected to multiparametricalloading. This method worked of by the author is based on the so-called „deformation map" which contains the whole information of the behaviour of the systflm subjected to three-parametrical loading. As a basic example taken the stability of geometrically nonlinear spherical shells subjected to transient pressure, contur external forces and temperature field. A number of new effects was revealed. The map call be applied lor any nonlinear system (even non elastic) which is described by means of differential equations.