Development of Boundary Element Method in Polar Coordinate System for Elasticity Problems

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Development of Boundary Element Method in Polar Coordinate System for Elasticity Problems

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Abstract

The article presents an exact version of the boundary element method, in particular, the fictitious load method used to solve boundary value and boundary-contact problems of elasticity. The method is developed in the polar coordinate system. The circular boundary of the area limited with the coordinate axes of this system is divided not into small segments like in case of a standard boundary element method (BEM), but into small arcs, while the linear part of the boundary divides into small segments. In such a case, the considered area can be described more accurately than when it divides into small segments, and as a result, a more accurate solution of the problem is obtained. Two test boundary-contact problems were solved by using a boundary element method developed in the polar coordinate system (PCSBEM), and the obtained numerical values are presented as tables and graphs.

References

25 Cites in Article
  1. 1. S Crouch,A Starfield (1983). Boundary element methods in solid mechanics. Boundary element methods in solid mechanics
  2. 2. C Brebbia,J Telles,L Wrobel (1984). Boundary element techniques: theory and applications in engineering. Boundary element techniques: theory and applications in engineering
  3. 3. Sara Moussawi,Joseph Mertz,Jeria Quesenberry,Xiaoying Tu,Julia Poepping,Larry Heimann,Raja Sooriamurthi,Divakaran Liginlal,Christopher Kowalsky,Martin Barrett,Gabriela Gongora-Svartzman,Oscar Veliz,Laura Pottmeyer,Michael Melville (1973). Building Future Information Systems Leaders: The Crucial Role of Problem Scoping in Service-Learning Experiences. Communications of the Association for Information Systems, 55, 946-977.
  4. 4. G Węcel (2006). BEM-FVM solution of the conjugate radiative and convective heat transfer problem. Archives of Computational Methods in Engineering, 13(2), 171-248.
  5. 5. J Chen,Lin Sy,Chen Lee,Y (2006). Mathematical analysis and numerical study to free vibrations of annular plates using BIEM and BEM. Int. J. Numer. Meth, 65, 236-263.
  6. 6. N Zirakashvili (2006). The numerical solution of boundary-value problems for an elastic body with an elliptic hole and linear cracks. Journal of Engineering Mathematics, 65(2), 111-123.
  7. 7. Zhu Song,-Ping,Zhang Yinglong (2007). Comparison of the BEM and DRBEM in solving the Helmholtz equation. ANZIAM J, 49, 131-150.
  8. 8. N Zirakashvili (2007). Numerical Analysis of the Stress Distribution by the Boundary Elements Method in Continuous Body with a Hole. Bull. Georg. Nat. Acad. Sci, 175(3), 22-25.
  9. 9. S Ahmed,S Meshrif (2009). A new numerical algorithm for 2D moving boundary problems using a boundary element method. Computers & Mathematics with Applications, 58(7), 1302-1308.
  10. 10. Unknown Title. J
  11. 11. N Zirakashvili,Janjgava (2009). Numerical Solution of Some Plane Boundary Value Problems of the Theory of Binary Mixtures by the Boundary Element Method. Applied Mathematics Informatics and Mechanics, 14(1), 79-95.
  12. 12. N Zirakashvili (2009). The numerical solution of boundary-value problems for an elastic body with an elliptic hole and linear cracks. Journal of Engineering Mathematics, 65(2), 111-123.
  13. 13. M Mohammadi,M Hematiyan,M Aliabadi (2010). Boundary element analysis of thermo-elastic problems with non-uniform heat sources. The Journal of Strain Analysis for Engineering Design, 45(8), 605-627.
  14. 14. N Khomasuridze,N Zirakashvili (2010). Strain control of cracked elasic bodies means of boundary condition variation. Proceedings of International Conference "Architecture and Construction -Contemporary Problems, 158-163.
  15. 15. Natela Zirakashvili (2010). Study of stress–strain state of elastic body with hyperbolic notch. Zeitschrift für angewandte Mathematik und Physik, 70(3), 138-143.
  16. 16. G Tsiatas,A Yiotis (2013). A BEM-based meshless solution to buckling and vibration problems of orthotropicplates. Engineering Analysis with Boundary Elements, 37(3), 579-584.
  17. 17. N Zirakashvili (2013). On the numerical solution of some two-dimensional boundary-contact delocalization problems. Meccanica, 48(7), 1791-1804.
  18. 18. Guo Zhao Liu Yijun,Ma Hang,Huang Shuo (2014). A fast multipole boundary element method for modeling 2-D multiple crack problems with constant elements. Engineering Analysis with Boundary Elements, 47, 1-9.
  19. 19. F Morcos,Mohammed Samaan,F Nassar ; ) Youssef,Rashed (2015). Taylor series fast multipole boundary element method for solution of Reissner's shear deformable plate bending problems. Engineering Analysis with Boundary Elements, 59, 23-35.
  20. 20. S Potapenko (2016). An integral representation for the solution of the inclusion problem in the theory of antiplane micropolar elasticity. Mathematics and Mechanics Solids, 23(4), 543-553.
  21. 21. J Lachat,J Watson (1976). Effective numerical treatment of boundary-integral equations: a formulation for tree-dimensional elastostatics. Int. J. Num. Methods Eng, 10, 991-1005.
  22. 22. S Timoshenko,J Goodier (1970). Theory of Elasticity. Timoshenko and Goodier . McGraw-Hill. New York 1951. 493 pp. 270 diagrams. 81s. net. (<i>New Edition</i>.). The Journal of the Royal Aeronautical Society, 56(496), 308-308.
  23. 23. N Nefedov,D Ramonas,B Khasanov,A Alexandrov (1958). Pharmacoeconomical approaches for assessing the rational use of ophthalmic drugs in polyclinic settings. Modern technologies in ophtalmology, 143-145.
  24. 24. J Jaeger (1962). Elasticity, fracture and flow, with engineering and geological applications. Elasticity, fracture and flow, with engineering and geological applications
  25. 25. Amenzade Yua,M Konyaeva (1979). Theory of elasticity. Theory of elasticity

Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

How to Cite This Article

Natela Zirakashvili. 2018. "Development of Boundary Element Method in Polar Coordinate System for Elasticity Problems". Global Journal of Research in Engineering - J: General Engineering GJRE-J Volume 18 (GJRE Volume 18 Issue J5).

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Journal Specifications

Crossref Journal DOI 10.17406/gjre

Print ISSN 0975-5861

e-ISSN 2249-4596

Keywords
Classification
GJRE-J Classification FOR Code: 010299
Version of record

v1.2

Issue date
December 8, 2018

Language
English
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Development of Boundary Element Method in Polar Coordinate System for Elasticity Problems

Natela Zirakashvili
Natela Zirakashvili I. Vekua Institute of Applied Mathematics of Iv. Javakhishvili Tbilisi State University