Fast multipole boundary element method for the analysis of plates with many holes

• Autorzy: Ptaszny J. , Fedeliński P.
• Konferencja: Solid Mechanics Conference (35 ; 04-08.09.2006 ; Cracow, Poland)
• Języki publikacji: EN

Abstrakty

EN

A three-node quadratic element version of the fast multipole boundary element method (FMBEM) for two-dimensional elastostatic problems is presented. The method is applied to the analysis of perforated plates. A comparison of convergence and accuracy of the present method using quadratic elements with the method using constant elements, presented by other authors, is given. Stress results for a square plate with a circular hole are investigated. Effective material properties of plates with many holes are estimated and compared to analytical results. Implementation of quadratic-element version of the FMBEM resulted in a lower number of degrees of freedom and expansion terms, and similar accuracy to constant-element version of the method, for the same structures. Influence of boundary conditions on the convergence of the iterative solver is investigated. The effectiveness of the FMBEM in relation to the conventional BEM is presented.

Słowa kluczowe

EN

elastostatics; fast multipole boundary element method; quadratic boundary element; porous material; effective material properties

PL

statyka; metoda elementów brzegowych; kwadratowy element brzegowy; materiał porowaty; własności materiałowe efektywne

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2007
• Tom: Vol. 59, nr 4-5
• Strony: 385--401
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Ptaszny J.

autor

Fedeliński P.

• Department of Strength of Materials and Computational Mechanics Silesian University of Technology ul. Konarskiego 18a, 44-100 Gliwice. Poland

Bibliografia

• 1. V. ROKHLIN, Rapid Solution of Integral Equations of Classical Potential Theory, J. Corn-put. Phys., 60, 187-207, 1985.
• 2. L. GREENGARD, V. ROKHLIN, A Fast Algorithm for Particle Simulations, J. Comp. Phys., 73, 325-348, 1987.
• 3. J. BARNES, P. HUT, A hierarchical O(N\ogN) force-calculation algorithm, Nature, 324, 4, 446-449,1986.
• 4. N. NISHIMURA, Fast multipole accelerated boundary integral equation methods, Appl. Mech. Rev., 55, 4, 299-324, 2002.
• 5. N. Hu, B. WANG, G. W. TAN, Z. H. YAO, W. F. YUAN, Effective elastic properties of 2-D solids with circular holes: numerical simulations, Comp. Sci. Techn., 60, 1811-1823, 2000.
• 6. H. WANG, Z. YAO, P. WANG, On the preconditioned for fast multipole boundary element methods for 2D multi-domain elastostatics, Eng. Anal. Boundary Elements, 29, 673-688, 2005.
• 7. Y. J. Liu, A new fast multipole boundary element method for solving large-scale two-dimensional elastostatic problems, Int. J. Numer. Meth. Engng., 65, 863-881, 2006.
• 8. J. PTASZNY, P. FEDELINSKI, Fast multipole boundary element method for two-dimensional elastostatic problems [in Polish], Engineering Modelling, 32, 1, 407-414, 2006.
• 9. J. BREBBIA, J. DOMINGUEZ, Boundary elements an introductory course, McGraw-Hill, New York 1992.
• 10. Y. YAMADA, K. HAYAMI, A multipole boundary element method for two-dimensional elastostatics, Tech. Report, METR 95-07, Math. Eng. Section, Dept. Math. Eng., Information Phys., Univ. Tokyo 1995.
• 11. Z, YAO, F, KONG, H, WANG, P. WANG, 2D Simulation of composite materials using BEM, Eng. Anal. Boundary Elements 28, 927-935, 2004.
• 12. M. KACHANOV, On the moduli of solids with cavities and cracks, Int. J. Fracture, 59, R17-R21,
• 13. V. G. KOUZNETSOVA, Computational homogenization for the multi-scale analysis of multiphase materials, Eindhoven, 2002,
• 14. L. H. DAI, Z, P, HUANG, R. WANG, Explicit expressions for bounds for the effective moduli of multi-phased composites by the generalized self-consistent method, Comp. Sci. TechiL, 59, 1691-1699,