Study on Stability for Compressive Elastic-Fixed Strip

Studies on the influence of various types of imperfections in elastic systems in the case of several external forces were analyzed. The analysis showed that in most studies, a loading function was introduced at a certain stage of research, and the loads ceased to be independent. The two most frequently used static stability criteria in the mechanics of deformable solids are the bifurcation criterion and criterion of the method of initial imperfections. It is shown that these are methods for finding singular points of the implicit function theorem (only those pairs of spaces with corresponding norms in which the derivative of the Fréchet map is an isomorphism are considered). Using this result, we analyzed the continuous dependence of the function describing the state of the compressed elastic strip on the characteristics of the initial imperfections. A condition is obtained that is imposed on the external influence parameter and base stiffness coefficient; if violated, the cross-sectional shape of the strip will no longer be close to a rectangle; that is, the strip loses its shape. Moreover, these parameters remained independent throughout the study. The new results were compared with known classical results.