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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2017, Volume 57, Number 7, Page 1230
DOI: https://doi.org/10.7868/S004446691707002X
(Mi zvmmf10593)
 

This article is cited in 5 scientific papers (total in 5 papers)

A theoretical measure technique for determining $3\mathrm{D}$ symmetric nearly optimal shapes with a given center of mass

H. D. Alimorad, A. J. Fakharzadeh

Shiraz University of Technology, Shiraz, Iran
Full-text PDF (29 kB) Citations (5)
Abstract: In this paper, a new approach is proposed for designing the nearly-optimal three dimensional symmetric shapes with desired physical center of mass. Herein, the main goal is to find such a shape whose image in $(r, \theta)$-plane is a divided region into a fixed and variable part. The nearly optimal shape is characterized in two stages. Firstly, for each given domain, the nearly optimal surface is determined by changing the problem into a measure-theoretical one, replacing this with an equivalent infinite dimensional linear programming problem and approximating schemes; then, a suitable function that offers the optimal value of the objective function for any admissible given domain is defined. In the second stage, by applying a standard optimization method, the global minimizer surface and its related domain will be obtained whose smoothness is considered by applying outlier detection and smooth fitting methods. Finally, numerical examples are presented and the results are compared to show the advantages of the proposed approach.
Key words: artificial control, center of mass, honey-bee-method, outlier detection, radon measure, symmetric three dimensional shape.
Received: 05.10.2014
Revised: 10.08.2015
English version:
Computational Mathematics and Mathematical Physics, 2017, Volume 57, Issue 7, Pages 1225–1240
DOI: https://doi.org/10.1134/S0965542517070028
Bibliographic databases:
Document Type: Article
UDC: 519.626
Language: English
Citation: H. D. Alimorad, A. J. Fakharzadeh, “A theoretical measure technique for determining $3\mathrm{D}$ symmetric nearly optimal shapes with a given center of mass”, Zh. Vychisl. Mat. Mat. Fiz., 57:7 (2017), 1230; Comput. Math. Math. Phys., 57:7 (2017), 1225–1240
Citation in format AMSBIB
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  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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