Assessment Criterion for Optimum Design Solutions of Piecewise Constant Sections in Rods of Rectangular Cross-Section With Stability or First Eigen-Frequency Limits

Abstract

Specific properties of optimum systems have been already considered in previous research. Moreover, the criteria were proposed for a correct assessment of proximity of optimum to minimum material consumption. In particular, the criteria are proposed for rods of rectangular crosssection with stability or first eigen-frequency limits. These criteria can be used for problem optimization, when the rod cross-sections continuously change longitudinally. The obtained optimum solutions can be considered as a perfect limited object. This optimum project function allows researcher to assess the real design solution using the proximity limit criterion (for example, material consumption limit). This kind of optimum design can also be used as a guideline for real design in terms of a stage-by-stage process of transition from a perfect to real object. In this case, it is possible to assess changes in the object optimality at each stage as compared to the initial and idealized solutions. In particular, one of the variants of the process includes replacing the rod with continuous longitudinally varying cross-sections by a rod with piecewise constant sections. The section boundaries can be based on a perfect object, and cross-sections can be determined by one of the optimization methods. This paper presents criteria, which ensure the reliable definition of the time of completion of the optimization process.