On One Problem of Optimization of Structures Considering the Requirements of Stability and Strength Under the Constraints of the First Frequency of Natural Vibrations

Abstract

In a previous paper the authors of this paper considered the problem of assessing the proximity of the decision to draft minimum material consumption by optimizing the width of the shelves bars beam cross-section subject to the limits of stability or values of the first natural frequency and the requirements of strength in the case of continuous changes of variable parameters along the length of the rod. In construction practice, as a rule, rods are designed with a piecewise constant change in the size of the section. Previously, the authors formulated a criterion for evaluating optimal solutions for the formation of piecewise constant sections of the I-beam shelf with restrictions on stability or the value of the first frequency of natural vibrations, while the strength of the rod was assumed to be secured. This article clarifies the criterion for the case when the strength requirements are considered in the optimization process.