Метод поиска оптимальной по стоимости траектории дороги на поверхности местности

Majid E. Abbasov; Artyom S. Sharlay

doi:10.21638/11701/spbu10.2023.201

Authors

Majid E. Abbasov St Petersburg State University, 7-9, Universitetskaya nab., St Petersburg, 199034, Russian Federation; Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences, 61, Bolshoy pr. V.O., St. Petersburg, 199178, Russian Federation
Artyom S. Sharlay St Petersburg State University, 7-9, Universitetskaya nab., St Petersburg, 199034, Russian Federation; Military Academy of Logistics (VAMTO named after A. V. Hrulev), 1, Suvorovskaya uh, Peterhof, St. Petersburg, 198504, Russian Federation

DOI:

https://doi.org/10.21638/11701/spbu10.2023.201

Abstract

The paper studies a method for finding the cost-optimal trajectory of a road connecting two points on a given terrain. Situations are considered when the cost of delivery of materials is a constant value, as well as a more general formulation of the problem, in which the cost of delivery depends on the coordinate of a point. In each case, an integral functional is constructed cost, the argument in which is a function that describes the trajectory of the path. The Ritz method is used to find an approximate solution. It is set analytically, in the form of a trigonometric polynomial, which increases the convenience of processing and further research of the results obtained in comparison with the numerical solution of the necessary conditions for the extremum of the investigated functional. The paper also discusses the problem of convergence. Illustrative examples are given.

Keywords:

calculus of variations, optimization, Ritz method, trigonometric polynomial

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References

Литература

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References

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Xue J., Wang Y. Free vibration analysis of a flat stiffened plate with side crack through the Ritz method. Arch. Appl. Mech., 2019, vol. 89, pp. 2089-2102.