Open AccessASSESSMENT CRITERIA OF OPTIMAL SOLUTIONS FOR CREATION OF RODS WITH PIECEWISE CONSTANT CROSS-SECTIONS WITH STABILITY CONSTRAINTS OR CONSTRAINTS FOR VALUE OF THE FIRST NATURAL FREQUENCY. PART 1: THEORETICAL FOUNDATIONS
Author(s) -
Leonid Lyakhovich,
Pavel А. Akimov,
Б. А. Тухфатуллин
Publication year - 2019
Publication title -
international journal for computational civil and structural engineering
Language(s) - English
Resource type - Journals
eISSN - 2588-0195
pISSN - 2587-9618
DOI - 10.22337/2587-9618-2019-15-4-88-100
Subject(s) - piecewise , limit (mathematics) , constant (computer programming) , mathematics , stability (learning theory) , mathematical optimization , process (computing) , ideal (ethics) , function (biology) , point (geometry) , computer science , mathematical analysis , geometry , philosophy , epistemology , machine learning , evolutionary biology , biology , programming language , operating system
The special properties of optimal systems have been already identified. Besides, criteria has been formulated to assess the proximity of optimal solutions to the minimal material consumption. In particular, the criteria were created for rods with rectangular and I-beam cross-section with stability constraints or constraints for the value of the first natural frequency. These criteria can be used for optimization when the cross sections of a bar change continuously along its length. The resulting optimal solutions can be considered as an idealized object in the sense of the limit. This function of optimal design allows researcher to assess the actual design solution by the criterion of its proximity to the corresponding limit (for example, regarding material consumption). Such optimal project can also be used as a reference point in real design, for example, implementing a step-bystep process of moving away from the ideal object to the real one. At each stage, it is possible to assess the changes in the optimality index of the object in comparison with both the initial and the idealized solution. One of the variants of such a process is replacing the continuous change in the size of the cross sections of the rod along its length with piecewise constant sections. Boundaries of corresponding intervals can be selected based on an ideal feature, and cross-section dimensions can be determined by one of the optimization methods. The distinctive paper is devoted to criteria that allow researcher providing reliable assessment of the endpoint of the optimization process.