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Numerical Solution of Two-Point Static Problems for Distributed Extended Systems by Means of the Nelder–Mead Method

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Cybernetics and Systems Analysis Aims and scope

Abstract

The authors describe a numerical algorithm for reducing two-point static problems of distributed extended systems in the field of body and surface forces to a nonlinear programming problem that can be solved by numerical methods. Variations in the dimension of the physical problem being solved do not change the entire numerical algorithm, but only lead to replacement of some of its blocks. Numerical examples illustrating the described algorithm are given. The problems of determining power and geometric characteristics of deep water intake of nuclear power plants, assessing the quality of the diverter and determining the stiffness coefficient of the anchor coupling of semi-submersible drilling platform are considered as examples of nonlinear programming problems.

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References

  1. B. Chen, F. Su, C. Huo, R. Zhang, B. Yao, and L. Lian, “Numerical investigation of the dynamics for low tension marine cables,” J. of Shanghai Jiaotong University (Science), Vol. 20, Iss. 3, 257–264 (2015). https://doi.org/10.1007/s12204-014-1559-6.

  2. T. Nimmy and T. Manoj, “Analysis of tow cables,” Universal J. of Mechanical Engineering, Vol. 5, No. 5, 144–149 (2017). https://doi.org/10.13189/ujme.2017.050502.

    Article  Google Scholar 

  3. O. M. Trofymchuk, Yu. I. Kaliukh, V. A. Dunin, and Y. A. Berchun, “On the possibility of multi-wavelength identification of defects in piles,” Cybern. Syst. Analysis, Vol. 54, No. 4, 600–609 (2018).

    Article  MATH  Google Scholar 

  4. H. Troger, A. P. Alperton, V. V. Beletsky, V. I. Dranovskii, V. S. Khoroshilov, A. V. Pirozhenko, and A. E. Zakrzhevskii, Dynamics of Tethered Space Systems (Advances in Engineering Series), CRC Press (2017).

  5. O. A. Goroshko and G. N. Savin, An Introduction to Mechanics of Deformable One-Dimensional Solids of Variable Length [in Russian], Naukova Dumka, Kyiv (1971).

    Google Scholar 

  6. R. L. Doyle and J. Halkyard, “Large scale airlift experiments for application to deep ocean mining,” Proc. 26th Intern. Conf. on Offshore Mechanics and Arctic Engineering (San Diego, CA, USA, June 10–15, 2007), American Society of Mechanical Engineers, New York (2007), pp. 27–36. https://doi.org/10.1115/OMAE2007-29641.

  7. V. A. Svetlitskii, Mechanics of Flexible Rods and Filaments [in Russian], Mashinostroenie, Moscow (1978).

    Google Scholar 

  8. A. V. Gladkii, I. V. Sergienko, and V. V. Skopetsky, Numerical and Analytical Methods for the Analysis of Wave Processes [in Russian], Naukova Dumka, Kyiv (2001).

    Google Scholar 

  9. I. V. Sergienko and V. S. Deineka, Optimal Control of Distributed Systems with Conjugation Conditions, Springer, New York (2005).

    MATH  Google Scholar 

  10. G. Farenyuk, I. Kaliukh, E. Farenyuk, T. Kaliukh, Y. Berchun, and V. Berchun, “Experimental and theoretical diagnostics of defects in ferroconcrete piles based on reflection of longitudinal and transverse waves,” in: D. Hordijk and M. Lukivić (eds), High Tech Concrete: Where Technology and Engineering Meet, Springer, Cham (2018), pp. 1307–1317.

    Chapter  Google Scholar 

  11. Yu. I. Kaliukh and A. Ye. Vusatiuk, “Factorization in problems of control and dynamics of lengthy systems,” Cybern. Syst. Analysis, Vol. 55, No. 2, 274–283 (2019).

    Article  Google Scholar 

  12. Iu. Kaliukh, “Statics, dynamics, and optimization of transportation cable systems in a flow,” Author’s PhD These, Ukrainian Correspondence Pedagogical Institute, Kharkiv (1993).

  13. D. M. Himmelblau, Applied Nonlinear Programming, McGraw-Hill (1972).

  14. P. P. Kul’mach, Anchor Systems to Hold Buoyant Objects [in Russian], Sudostroenie, Leningrad (1980).

    Google Scholar 

  15. V. I. Egorov, Underwater Towed Systems [in Russian], Sudostroenie, Leningrad (1981).

    Google Scholar 

  16. K. Yoshida, T. Yoneya, and K. Ida, “Static and dynamic analysis of underwater line structures by the finite element methods,” J. Soc. Nav. Arhit. Jap., Vol. 144, 195–204 (1978).

    Article  Google Scholar 

  17. Building Codes and Regulations (SniP) 2.06.04-82. Loads and Effects on Hydraulic Engineering Structures (Wave, Ice, and from Ships), Gosstroi USSR, Stroiizdat, Moscow (1983).

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Authors and Affiliations

  1. State Enterprise “State Research Institute of Building Constructions” and Institute of Telecommunications and Global Information Space, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    Iu. Kaliukh

  2. Institute of Telecommunications and Global Information Space, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    O. Trofymchuk & O. Lebid

Authors
  1. Iu. Kaliukh
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  2. O. Trofymchuk
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  3. O. Lebid
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Corresponding author

Correspondence to Iu. Kaliukh.

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Translated from Kibernetika i Sistemnyi Analiz, No. 4, July–August, 2019, pp. 109–118.

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Kaliukh, I., Trofymchuk, O. & Lebid, O. Numerical Solution of Two-Point Static Problems for Distributed Extended Systems by Means of the Nelder–Mead Method. Cybern Syst Anal 55, 616–624 (2019). https://doi.org/10.1007/s10559-019-00170-3

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  • DOI: https://doi.org/10.1007/s10559-019-00170-3

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