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Method of fundamental solutions and random numbers for the torsion of bars with multiply connected cross sections

Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The torsion of bars with multiply connected cross section by means of the method of fundamental solutions (MFS) is considered. Random numbers were used to determine the minimal errors for MFS. Five cases of cross sections are examined. The numerical results for different cross sectional shapes are presented to demonstrate the efficiency and accuracy of the method. Non-dimensional torsional stiffness was calculated by means of numerical integration of stress function for one of the cases. This stiffness was compared with the exact stiffness for the first case and with the stiffness resulting from Bredt's formulae for thin-walled cross sections.
Rocznik
Strony
99--112
Opis fizyczny
Bibliogr. 27 poz., rys., tab., wykr.
Twórcy
Bibliografia
  • [1] E. Weinel. The torsion problem for the eccentric annulus (in German). Ingenieur Archivs, 3: 67-75, 1932.
  • [2] G. Polya, A. Weinstein. On the torsion rigidity of multiply connected cross-sections. Annals of Mathematics, 52: 154-163, 1950.
  • [3] N.H. Arutyunyan, B.L. Abrahamian. Torsion of elastic body (in Rusian). Gosudarstvennoe Izdatelstvo Fiziko-Matematicheskoj Literatury, Moskwa, 1963.
  • [4] C.Y. Wang. Torsion of a flattened tube. Meccanica, 30: 221-227, 1995.
  • [5] C.Y. Wang. Torsion of tubes of arbitrary shape. International Journal Solids Structures, 35: 719-731, 1998.
  • [6] Y. Y. Kim, M.S. Yoon. A modified Fourier series method for the torsion analysis of bars with multiply connected cross sections. International Journal Solids Structures, 34: 4327-4337, 1997.
  • [7] G. Mejak. Optimization of cross-section of hollow prismatic bars in torsion. Communications in Numerical Methods in Engineering, 16: 687-695, 2000.
  • [8] J.A. Kolodziej, A. Fraska. Elastic torsion of bars possessing regular polygon in cross-section, Computers &Structures, 84: 78-91, 2005.
  • [9] Z. Dyląg, A. Jakubowicz, Z. Orlos. Mechanics of materials (in Polish), volume I. WNT, Warszawa, 1999.
  • [10] A. Morassi. Torsion of thin tubes with multicell cross-section. Meccanica, 34: 115-132, 1999.
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  • [12] M.R. Hematiyan, A. Doostfatemeh. Torsion of moderately thick hollow tubes with polygonal shapes. Mechanics Research Communications, 34: 528 537, 2007.
  • [13] V.D. Kupradze, M.A. Aleksidze. The method of functional equations for the approximate solution of certain boundary value problems (in Rusian). Zurnal Vycislennoj Matematiki i Matetyczeskoj Fizyki, 4: 683-715, 1964.
  • [14] R. Mathon, R.L. Johnston. The approximate solution of elliptic boundary value problems by fundamental solutions. SIAM Journal on Numerical Analysis, 14: 638-650, 1977.
  • [15] A. Bogomolny. Fundamental solution method for elliptic boundary value problems. SIAM Journal on Numerical Analysis, 22: 644-669, 1985.
  • [16] M. Katsurada. Asymptotic error analysis of the charge simulation method. Journal of the Faculty of Science. University of Tokyo, Section 1 A, 37: 635-657, 1990.
  • [17] M. Katsurada, H. Okamoto. A mathematical study of the charge simulation method. Journal of the Faculty of Science. University of Tokyo, Section 1A, 35: 507-518, 1988.
  • [18] M. Katsurada, H. Okamoto. The collocation points of the fundamental solution method for the potential problem. Computers & Mathematics with Applications, 31: 123-137, 1996.
  • [19] T. Kitagawa. Asymptotic stability of the fundamental solution method. Journal of Computational and Applied Mathematics, 38: 263-69, 1991.
  • [20] T. Kitagawa. 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, 1988.
  • [21] G. Fairweather, A. Karageorghis. The method of fundamental solutions for elliptic boundary value problems. Advances in Computational Mathematics, 9: 69-95, 1998.
  • [22] M.A. Golberg, C.S. Chen. The method of fundamental solutions for potential, Helmholtz and diffusion problems. In: M.A. Golberg, editor. Boundary integral methods - numerical and mathematical aspects, 103-176. Boston, Computational Mechanics Publications, 1998.
  • [23] K.H. Chen, J.H. Kao, J.T. Chen, D.L. Young, M.C. Lu. Regularized meshless method for multiply connected domain Laplace problems. Engineering Analysis with Boundary Elements, 30: 882-896, 2006.
  • [24] Z-C. Li. The method of fundamental solutions for annular shaped domains. Journal of Computational and Applied Mathematics, I: 355-372, 2009.
  • [25] Th. Tsangaris, Y. S. Smyrilis, A. Karageorghis. Numerical analysis of the method of fundamental solutions forharmonic and biharmonic problems in annular domains. Numerical Method for Partial Differential Equations, 22: 507-539, 2006.
  • [26] N.H. Arutyunyan, B.L. Abrahamian. Torsion of prismatic rods (in Rusian). Erevan, 1962.
  • [27] P. Gorzelanczyk, J.A. Kolodziej. Some remarks concerning the shape of the source contour with application of the method of fundamental solutions to elastic torsion of prismatic rods. Engineering Analysis with Boundary Elements, 24: 633-641, 2007.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPB8-0022-0002
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