ON THE OPTIMAL POSITION OF THE INTERMEDIATE SUPPORT OF THE COMPRESSED THREE-SPAN ROD AND ITS QUALITATIVE FEATURES

Abstract

The optimization problem is considered, which consists in maximizing the main critical force of a three-span longitudinally compressed rod supported at the ends on absolutely rigid hinge supports due to the optimal choice of the position of one of the intermediate supports. It is known that in many cases this position is a node of the buckling form, which corresponds to the second critical force in the spectrum of the two-span rod formed by removing the moving support. A range of recent studies have described cases where the maximum critical force is reached at other positions. This, in particular, occurs at a finite stiffness of one or both end supports of the rod. The proposed work seeks the optimal position of the rigid intermediate support, provided that the second intermediate support has a finite stiffness and a fixed position. The compressive force is assumed to be constant along the length of the rod, bending stiffness can vary according to the length of the rod according to arbitrary way. It is established that under certain conditions the solution of this problem can be reduced to the solution of another, previously studied problem, which seeks the maximum critical force of a two-span rod by changing its length, at which some segment of the rod adds or removes at one end of the rod with the transfer of the corresponding hinged support at the end of the newly created rod. The paper founds and describes the characteristic qualitative features of the buckling forms, which correspond to the maximum of the main critical force, in particular the absence of deformation of the bending of the end span adjacent to the moving support. The limitations in which the approach proposed in the paper leads to the determination of the desired optimal position of the movable support are studied. The results are obtained mainly on the basis of the systematic use of qualitative methods and allow to obtain qualitative estimates for the localization of the moving support and the value of the corresponding critical force. An example illustrating the proposed approach and the reliability of the results of its application are considered.