Using the Criterion of the Minimum Material Capacity of Rods Under Stability Restrictions for the Case of Multiple Critical Load

As it is known, special criteria are formulated to evaluate the obtained solution of some optimization problems. In particular, we formulate a criterion that allows us to estimate the proximity of the decision on the rod of the lowest weight and the restrictions on the resistance to the minimum material-intensive for rectilinear rods for certain types of cross sections. The criterion is based on the analysis of stresses from bending moments arising from the loss of stability. If the least critical force is not a multiple, then the form of loss of stability and the corresponding diagram of moments are the only ones. At multiplicity of the least critical load there are multiple forms of loss of stability, and any of their linear combination is also its own form. To estimate the obtained solution, it is necessary to form a combination of multiple forms of buckling and the corresponding diagram of bending moments, which will serve as the basis for the use of the criterion. This paper proposes an approach that allows to determine such a combination of multiple forms, which will be the basis for the application of the criterion of proximity of the obtained solution to the minimum material-intensive.