Calculation of nonlinear covers deformation with the developed median surface the approached analytical methods

Authors

  • Игорь Васильевич Андрианов Институт общей механики высшей технической школы Земля Южный Рейн-Вестфалия, Templergraben 64, Ахен, D-52062, Germany
  • Анатолий Михайлович Мильцын ТД Днепропетровский завод сварочных материалов, Ukraine
  • Виктор Исаакович Олевский ТД Днепропетровский завод сварочных материалов, Ukraine
  • Владислав Валентинович Плетин ТД Днепропетровский завод сварочных материалов, Ukraine

DOI:

https://doi.org/10.15587/1729-4061.2010.2890

Keywords:

shells, developable surface, the parameter continuation, Padé approximants

Abstract

An analysis of the approximate analytical calculation of the displacements of inhomogeneously loaded shells with developable principal surface by means of modified methods of Adomian's decomposition, homotopy perturbation and the parameter continuation was represented, taking into account the geometric nonlinearity. A generalized summation of the solutions was used based on one-and two-dimensional Pade approximants.

Author Biographies

Игорь Васильевич Андрианов, Институт общей механики высшей технической школы Земля Южный Рейн-Вестфалия, Templergraben 64, Ахен, D-52062

Доктор физико-математических наук, профессор

Анатолий Михайлович Мильцын, ТД Днепропетровский завод сварочных материалов

Кандидат технических наук, профессор, начальник отдела

Виктор Исаакович Олевский, ТД Днепропетровский завод сварочных материалов

Кандидат технических наук, заместитель директора

Владислав Валентинович Плетин, ТД Днепропетровский завод сварочных материалов

Инженер-математик, научный сотрудник

References

  1. Дородницын А.А. Применение метода малого параметра к численному решению дифференциальных уравнений // Соврем. проблемы матем. физики и вычисл. матем. М.: Наука, 1982. С.145-155.
  2. Adomian G. A review of the decomposition method and some recent results for nonlinear equations// Comp. Math. Appl. 1989. Vol.21. P.101-127.
  3. Андрианов И.В., Олевский В.И., Токажевский С. Модифицированный метод декомпозиции Адомяна//ПММ. 1998. Том 62, №.2. С. 334-339.
  4. He J.H. Recent developments of the homotopy perturbation method// Top. Meth. Nonlin. Anal. 2008. Vol.31. P. 205-209.
  5. Андрианов И.В. Применение метода Паде-аппроксимант для устранения неоднородностей асимптотических разложений // Изв. АН СССР. Механика жидкости и газа. 1984. №3. С.166-167.
  6. Vavilov V.V., Tchobanou M.K., Tchobanou P.M. Design of multidimensional Recursive Systems through Pad
  7. Wasov W. Asymptotic Expansions for Ordinary Differential Equations. New York: John Wiley & Sons, 1965. 464 p.
  8. Chrysos M., Sanchez F., Cherruault Y. Improvement of convergence of Adomian’s method using Pade
  9. Григолюк Э.И., Шалашилин В.И. Проблемы нелинейного деформирования: Метод продолжения решения по параметру в нелинейных задачах механики деформируемого твердого тела. М.: Наука, Гл. ред. физ.-мат. лит., 1988. 232 с.
  10. Орлов В.Н. Критерий существования подвижных особых точек решений дифференциального уравнения Риккати //Вестник СамГУ. Естественнонаучная серия. 2006. №6/1(46). С. 64-69.
  11. Andrianov, I.V., Kholod, E.G., Olevsky, V.I. “Approximate non-linear boundary value problems of reinforced shell dynamics», J. Sound Vibr., 1996. vol. 194, N 3, pp. 369 - 387.

Downloads

Published

2010-05-28

How to Cite

Андрианов, И. В., Мильцын, А. М., Олевский, В. И., & Плетин, В. В. (2010). Calculation of nonlinear covers deformation with the developed median surface the approached analytical methods. Eastern-European Journal of Enterprise Technologies, 3(9(45), 27–34. https://doi.org/10.15587/1729-4061.2010.2890

Issue

Vol. 3 No. 9(45) (2010): Applied mechanics

Section

Applied mechanics

License

Copyright (c) 2014 Игорь Васильевич Андрианов, Анатолий Михайлович Мильцын, Виктор Исаакович Олевский, Владислав Валентинович Плетин

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.

A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.