Method of fundamental solution and genetic algorithms for torsion of bars with multiply connected cross sections

• Autorzy: Gorzelańczyk P.

Warianty tytułu

PL

Zastosowanie metody rozwiązań podstawowych oraz algorytmów genetycznych do zagadnienia skręcania prętów o przekroju wielospójnym

• Języki publikacji: EN

Abstrakty

EN

The torsion of bars with a multiply connected cross sections by means of the method of fundamental solutions (MFS) is considered herein. To determine the optimal parameters of MFS, genetic algorithms were used. Seven cases of cross sections are considered. The numerical results for different cross sectional shapes are presented to demonstrate the efficiency and accuracy of the method. Non-dimension torsional stiffness was calculated by means of numerical integration of the stress function for one of the cases. This stiffness is compared with the exact stiffness for the first case and with the stiffness resulting from Bredt’s formulae for thin walled cross sections.

PL

W artykule rozważano skręcanie pretów z wielospójnym przekrojem poprzecznym za pomocą metody rozwiązań podstawowych (MRP). Do wyznaczenia optymalnych parametrów MRP wykorzystano algorytmy genetyczne. W pracy rozważano siedem problemów testowych. Bezwymiarowe sztywności skręcania liczono za pomocą numerycznego całkowania funkcji naprężeń dla jednego z przypadków. Te sztywności porównywano ze ścisłą sztywnością dla pierwszego przypadku i ze sztywnością uzyskaną ze wzoru Bredta dla cieńkich przekrojów poprzecznych.

Słowa kluczowe

EN

Bredt's formulae; method of fundamental solutions; multiply connected sections; genetic algorithms

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2011
• Tom: Vol. 49 nr 4
• Strony: 1059--1078
• Opis fizyczny: Bibliogr. 36 poz., rys., tab.

Twórcy

autor

Gorzelańczyk P.

• Higher Vocational State School Pila, Polytechnic Institute, Piła, Poland,

Bibliografia

• 1. Arutiunian N.H., Abramian B.L., 1962, Torsion of Prismatic Bars, AN SSSR, Erevan
• 2. Arutiunian N.H., Abramian B.L., 1963, Torsion of Elastic Body, Gosudarstvennoe Izdatelstvo Fiziko-Matematicheskoˇı Literatury, Moskva
• 3. Bogomolny A., 1985, Fundamental solution method for elliptic boundary value problems, SIAM Journal on Numerical Analysis, 22, 644-669
• 4. Bredt R., 1896, Kritische Bemerkungen zur drehungselastizitat, Zeitschrift des Vereines Deutscher Ingenieure, 40, 785-790
• 5. Chen K.H., Kao J.H., Chen J.T., Young D.L., Lu M.C., 2006, Regularized meshless method for multiply-connected-domain Laplace problems, Engineering Analysis with Boundary Elements, 30, 882-896
• 6. Dyląg Z., Jakubowicz A., Orłoś Z., 1999, Wytrzymałość materiałow, tom I, Wydawnictwo Naukowo-Techniczne, Warszawa
• 7. Fairweather G., Karageorghis A., 1988a, The almansi of fundamental solutions for numerical solution of the biharmonic equation, International Journal for Numerical Methods in Engineering, 26, 1668-1682
• 8. Fairweather G., Karageorghis A., 1998b, The method of fundamental solutions for elliptic boundary value problems, Advances in Computational Mathematics, 9, 69-95
• 9. Fairwearther G., Karageorghis A., 1989, The simple layer potential method of fundamental solutions for certain biharmonic equations, International Fluids for Numerical Methods in Fluids, 9, 1221-1234
• 10. Fairweather G., Karageorghis A., Martin P.A., 2003, The method of fundamental solutions for scattering and radiation problems, Engineering Analysis with Boundary Elements, 27, 759-769
• 11. Goldberg D.E., 1995, Algorytmy genetyczne i ich zastosowania, Wydawnictwo Naukowo-Techniczne, Warszawa
• 12. Golberg M.A., Chen C.S., 1998, The method of fundamental solutions for potential, Helmholtz and diffusion problems, [In:] Boundary Integral Methods – Numerical and Mathematical Aspects, Golberg M.A. (Edit.), Boston, Computational Mechanics Publications, 103-176
• 13. Hematiyan M.R., Doostfatemeh A., 2007, Torsion of moderately thick hollow tubes with polygonal shapes, Mechanics Research Communications, 34, 528-537
• 14. Karageorghis A., 2009, A practical algorithm for determining the optimal pseudo-boundary in the method of fundamental solutions, The Advances in Applied Mathematics and Mechanics, 1, 4, 510-528
• 15. Katsurada M., 1990, Asymptotic error analysis of the charge simulation method, Journal of the Faculty of Science, University of Tokyo, Section 1A, 37, 635-657
• 16. Katsurada M., Okamoto H., 1988, A mathematical study of the charge simulation method, Journal of the Faculty of Science, University of Tokyo, Section 1A, 35, 507-518
• 17. Katsurada M., Okamoto H., 1996, The collocation points of the fundamental solution method for the potential problem, Computers and Mathematics with Applications, 31, 123-137
• 18. Kim Y.Y., Yoon M.S., 1997, A modified Fourier series method for the torsion analysis of bars with multiply connected cross sections, International Journal Solids Structures, 34, 4327-4337
• 19. Kitagawa T., 1988, On the numerical stability of the method of fundamental solutions applied to the Dirichlet problem, Japan Journal of Industrial and Applied Mathematics, 35, 507-518
• 20. Kitagawa T., 1991, Asymptotic stability of the fundamental solution method, Journal of Computational and Applied Mathematics, 38, 263-69
• 21. Kołodziej J.A., Fraska A., 2005, Elastic torsion of bars possessing regular polygon in cross-section, Computers and Structures, 84, 78-91
• 22. Kołodziej J.A., Klekiel T., 2008, Optimal parameters of method of fundamental solutions for Poisson problems in heat transfer by means of genetic algorithms, Computer-Assisted Mechanics and Engineering Sciences, 15, 99-112
• 23. Kupradze V.D., Aleksidze M.A., 1964, The method of functional equations for the approximate solution of certain boundary-value problems, Zurnal Vychislennoˇı Matematiki i Matematycheskoˇı Fizyki, 4, 683-715 [in Rusian]
• 24. Li Z.-C., 2009, The method of fundamental solutions for annular shaped domains, Journal of Computational and Applied Mathematics, 1, 355-372
• 25. Lubarda V.A., 2009, On the torsion constant of multicell profiles and its maximization, Thin-Walled Structures, 47, 798-806
• 26. Mathon R., Johnston R.L., 1977, The approximate solution of elliptic boundary-value problems by fundamental solutions, SIAM Journal on Numerical Analysis, 14, 638-650
• 27. Mejak G., 2000, Optimization of cross-section of hollow prismatic bars in torsion, Communications in Numerical Methods in Engineering, 16, 687-695
• 28. Morassi A., 1999, Torsion of thin tubes with multicell cross-section, Meccanica, 34, 115-132
• 29. Nishimura R., Nishimori K., Ishihara N., 2000, Determining the arrangement of fictious charges in charge simulation method using genetic algorithm, Journal of Electrostatic, 49, 95-105
• 30. Nishimura R., Nishimori K., Ishihara N., 2001, Automatic arrangement of fictitious charges and contour points in charge simulation method for polar coordinate system, Journal of Electrostatics, 51/52, 618-624
• 31. Nishimura R., Nishihara M., Nishimori K., Ishihara N., 2003, Automatic arrangement of fictitious charges and contour points in charge simulation method for two spherical electrodes, Journal of Electrostatics, 57, 337-346
• 32. Polya G., Weinstein A., 1950, On the torsion rigidity of multiply connected cross-sections, Annals of Mathematics, 52, 154-163
• 33. Tsangaris Th., Smyrilis Y. S., Karageorghis A., 2006, Numerical analysis of the method of fundamental solutions for harmonic and biharmonic problems in annular domains, Numerical Method for Partial Differential Equations, 22, 507-539
• 34. Wang C.Y., 1995, Torsion of a flattened tube, Meccanica, 30, 221-227
• 35. Wang C.Y., 1998, Torsion of tubes of arbitrary shape, International Journal Solids Structures, 35, 719-731
• 36. Weinel E., 1932, Das Torsionsproblem fr den exzentrischen Kreisring, Ingenieur Archivs, 3, 67-75