On the influence of the paths of conservative multiparametrical loading on equilibrium states of geometrically nonlinear structures

Abstract

The problem of behaviour of nonlinear structures and systems subjected to multiparametrical excitations (loadings) is an important one both from theoretical and practical points of view. It is well known that there exist, as a rule, many possible different equilibrium states of this structure, all of which are generated by the same set of given values of loading parameters. The uniqueness of the solutions of equations of statical deformations does not take place due to the nonlinearity of the structures in question. It is natural to expect the existence of influence of multiparametrical loading paths on the final equilibrium state of the nonlinear structure. This phenomenon can be investigated, due to its nature, as a process only. That is by dynamic approach, when the equilibrium states are the steady ones. From the other side, incremental methods of numerical solutions of statical problems have similar lines with the dynamical approach. At the best knowledge of the author there is only one publication where this was done; the first attempt to discuss this phenomenon. In the present paper are described results of qualitative and numerical investigations of the phenomenon in question, and some of its general features. It was established in particular the existence of deep connection between the influence of above-mentioned loading paths on the behaviour of structures, and incremental algorithms of numerical solutions realized by FEM, finite difference methods or others. Without taking into consideration this phenomenon is very difficult to analyse the behaviour of multiparametrical excitated nonlinear structures, and to build the corresponding strategy for numerical solutions.