ASSESSMENT OF THE PROXIMITY OF DESIGN TO MINIMUM MATERIAL CAPACITY SOLUTION OF PROBLEM OF OPTIMIZATION OF THE FLANGE WIDTH OF I-SHAPED CROSS-SECTION RODS WITH ALLOWANCE FOR STABILITY CONSTRAINTS OR CONSTRAINTS FOR THE VALUE OF THE FIRST NATIONAL FREQUENCY AND STRENGTH REQUIREMENTS

Abstract

There are known methods for optimizing the flange width of I-shaped cross-section rods with stability constraints or the constraints for the value of the first natural frequency. Corresponding objective function has the form of the volume of the flange material for the case when only the flange width varies and the cross-section height, wall thickness and flange thickness are specified. Special criterion for assessment of proximity of corresponding an optimal solution to the design of minimal material capacity was formulated for the considering problem. In this case, the resulting solution may not meet some other unaccounted constraints, for example, strength requirements. Modification of solution in order to meet previously unaccounted constraints does not allow researcher to consider such design as optimal. In the distinctive paper allowance for strength requirements, stability constraints or constraints for the value of the first natural frequency are proposed within considering problem of optimization. Special approach is formulated, which proposes to assess proximity to the design of minimum of material capacity obtained as a result of optimization. Increment of the objective function and criteria corresponding to constrains and restrictions are under consideration within computational process.