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Shape identification in nonlinear boundary problems solved by pies method

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The paper presents the strategy for identifying the shape of defects in the domain defined in the boundary value problem modelled by the nonlinear differential equation. To solve the nonlinear problem in the iterative process the PIES method and its ad-vantages were used: the efficient way of the boundary and the domain modelling and global integration. The identification was performed using the genetic algorithm, where in connection with the efficiency of PIES we identify the small number of data required to the defect’s definition. The strategy has been tested for different shapes of defects.
Rocznik
Strony
16--21
Opis fizyczny
Bibliogr. 23 poz., rys., tab., wykr.
Twórcy
autor
  • Faculty of Mathematics and Informatics, University of Bialystok, ul. Sosnowa 64, 15-887 Bialystok, Poland
autor
  • Faculty of Mathematics and Informatics, University of Bialystok, ul. Sosnowa 64, 15-887 Bialystok, Poland
autor
  • Faculty of Mathematics and Informatics, University of Bialystok, ul. Sosnowa 64, 15-887 Bialystok, Poland
Bibliografia
  • 1. Ameen M. (2001), Boundary element analysis. Theory and pro-gramming, Alpha Science International Ltd.
  • 2. Aparicio N. D., Pidcock M. K. (1996), The boundary inverse prob-lem for the Laplace equation in two dimensions, Inverse Problems, 12, 565-577. 3. Bołtuć A., Zieniuk E. (2011a), Modeling domains using Bézier surfaces in plane boundary problems defined by the Navier-Lame equation with body forces, Engineering Analysis with Boundary Ele-ments, 35, 1116-1122. 4. Bołtuć A., Zieniuk E. (2011b), PIES in problems of 2D elasticity with body forces on polygonal domains, J. Theor. Appl. Mech., 49/2, 369-384.
  • 5. Cerrolaza M., Annicchiarico W., Martinez M. (2000), Optimization of 2D boundary element models using B-splines and genetic algo-rithms, Engineering Analysis with Boundary Elements, 24, 427-440.
  • 6. Cholewa R., Nowak A. J., Bialecki R. A., Wrobel L. C. (2002), Cubic Bézier splines for BEM heat transfer analysis of the 2-D con-tinuous casting problems, Computational Mechanics 28, 282-290.
  • 7. Durodola J. F., Fenner R. T. (1990), Hermitian cubic boundary elements for two-dimensional potential problems, International Jour-nal for Numerical Methods in Engineering, 30/5, 1051-1062.
  • 8. Farin G. (1990), Curves and Surfaces for computer Aided Geometric Design, Academic Press Inc., San Diego.
  • 9. Foley J., van Dam A., Feiner S., Hughes J., Phillips R. (1994), Introduction to Computer Graphics, Addison-Wesley.
  • 10. Goldberg D.E. (1989), Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley Publishing Company, Mas-sachusetts.
  • 11. Ligget J. A., Salmon J. R. (1981), Cubic spline boundary element, International Journal for Numerical Methods in Engineering, 17, 543-556.
  • 12. Liu G.R., Han X. (2003), Computational inverse techniques in non-destructive evaluation, CRC Press LLC.
  • 13. Michalewicz Z. (1996), Genetic Algorithms + Data Structures = Evolution Programs, Springer-Verlag, Berlin.
  • 14. Nowak I., Nowak A. J., Wrobel L. C. (2002) Identification of phase change front by Bézier splines and BEM, International Journal of Thermal Sciences, 41, 492-499.
  • 15. Rus G., Gallego R. (2002), Optimization algorithms for identification inverse problems with the boundary element method, Engineering Analysis with Boundary Elements, 26, 315-327.
  • 16. Sen D. (1995), A cubic-spline boundary integral method for two-dimensional free-surface flow problems. International Journal for Numerical Methods in Engineering, 38/11, 1809-1830.
  • 17. Tikhonov A.N., Arsenin V.Y. (1977), Solution of Ill-posed problems, John Wiley & Sons, New York.
  • 18. Wall M. (1996), GAlib: A C++ Library of Genetic Algorithm Compo-nents, version 2.4, Mechanical Engineering Department, Massachu-setts Institute of Technology (http://lancet.mit.edu/ga/).
  • 19. Zhu T., Zhang J., Atluri N. (1998), A meshless local boundary integral equation (LBIE) method for solving nonlinear problems, Computational Mechanics, 22, 174-186.
  • 20. Zieniuk E. (2007), Modelling and effective modification of smooth boundary geometry in boundary problems using B-spline curves, Engineering with Computers, 23/1, 39-48.
  • 21. Zieniuk E., Bołtuć A. (2006), Bézier curves in the modeling of boundary geometry for 2D boundary problems defined by Helm-holtz equation, Journal of Computational Acoustics, 14/3, 353-367.
  • 22. Zieniuk E., Bołtuć A. (2010), Iterative solution of linear and nonline-ar boundary problems using PIES, Lecture Notes in Computer Sci-ence, 6067, 136-145.
  • 23. Zienkiewicz O. (1977), The Finite Element Methods, McGraw-Hill, London.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-6d087421-b467-4ce7-8147-f85e3ec370f3
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