Quasi-static approach to non-conservative problems of the elastic stability theory

An elastic system loaded with the following forces is in an equilibrium state. Stability of this state in the small is investigated under the assumption that if this state is disturbed and the system is set into motion, there appear some small forces of a type unknown in advance. Stability of non-conservative elastic systems is usually analysed on the basis of dynamic approach only, that is, by means of composing equations of disturbed motion and investigating these equations. Such an approach does not conform to the considered system as the unknown type of small forces does not permit the formulation of equations of motion. For this reason, the problem of stability analysis is de®ned in the article in a new fashion. A quasi-static approach based on energy considerations is worked out. The approach results in the same buckling criterion as is used by the static energy method