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In this paper a fast multipole boundary element method (FMBEM) analysis of internal stress in two-dimensional linear elastic structures is presented. The expansions of the potentials occurring in the stress integral equation are obtained by the differentiation of local series built for the displacement eąuation potentials, and application of the strain-displacement and stress-strain relations. Results of the analysis are presented. To illustrate the accuracy of the method a stress concentration problems are considered, which are a square plate with a circular hole under tension, and a gear. The application of the FMBEM can reduce the analysis time in relation to the conventional BEM case, providing similar accuracy. Presented method can be applied in the BEM analysis of non-linear structures, which requires the evaluation of internal strains or stresses.
Rocznik
Tom
Strony
223--240
Opis fizyczny
Bibliogr. 22 poz., rys., tab., wykr.
Twórcy
autor
autor
- Department of Strength of Materials and Computational Mechanics, Silesian University of Technology, ul. Konarskiego 18A, 44-100 Gliwice, Poland, jacek.ptaszny@polsl.pl
Bibliografia
- [1] R. Beatson, L. Greengard. A short course on fast multipole methods. http: //www.math.nyu.edu/faculty/greengar/
- [2] C.A. Brebbia, J. Dominguez. Boundary elements an introductory course. McGraw-Hill, New York, 1992.
- [3] J. Engłund, J. Helsing. Stress computations on perforated polygonal domains. Eng. Anal. Bound. Elem., 27: 533-546, 2003.
- [4] L. Greengard, V. Rokhlin. A fast algorithm for particle simulations. J. Comput. Phys., 73: 325-348, 1987.
- [5] T. Lei, Z. Yao, H. Wang, P. Wang. A parallel fast multipole BEM and its applications to large-scale analysis of 3-D fiber-reinforced composites. Acta Mech. Sinica, 22: 225-232, 2006.
- [6] 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.
- [7] Y.J. Liu. A fast multipole boundary element method for 2D multi-domain elastostatic problems based on a dual BIE formulation. Comput. Mech., 42: 761-773, 2008.
- [8] Y.J. Liu, N. Nishimura, Y. Otani. Large-scale modeling of carbon-nanotube composites by a fast multipole boundary element method. Comput Mater. Sci., 34: 173-187, 2005.
- [9] Y.J. Liu, N. Nishimura, Y. Otani, T. Takahashi, X.L. Chen, H. Munakata. A fast boundary element method for the analysis of fiber-reinforced composites based on a rigid-inclusion model. J. Appl. Mech., 72: 115-128, 2005.
- [10] N. Nishimura. Fast multipole accelerated boundary integral eąuation methods. Appl. Mech. Rev., 55: 299-324, 2002.
- [11] G. Of, O. Steinbach, W.L. Wendland. Applications of a fast multipole Galerkin boundary element method in linear elastostatics. Bericht 2004/09, SFB 404, Universitat Stuttgart, 2004.
- [12] J. Ptaszny, P. Fedeliński. Fast multipole boundary element method for the analysis of plates with many holes. Arch. Mech., 59: 385-401, 2007.
- [13] J. Ptaszny, P. Fedeliński. Fast multipole boundary element method in analysis of structures loaded by volume forces (in Polish). Engineering Modeling, 35: 107-114, 2008.
- [14] H. Wang, Z. Yao, P. Wang. On the preconditioners for fast multipole boundary element methods for 2D multi-domain elastostatics. Eng. Anal. Bound. Elem., 29: 673-688, 2005.
- [15] H.T. Wang, Z.H. Yao. A new fast multipole boundary element method for large scale analysis of mechanical properties in 3D particle-reinforced composites. CMES - Comp. Model. Eng., 7: 85-95, 2005.
- [16] P.B. Wang, Z.H. Yao, Fast multipole boundary element analysis of two-dimensional elastoplastic problems. Commun. Numer. Meth. Engng., 23: 889-903, 2007.
- [17] P.B. Wang, Z.H. Yao. Application of a new fast multipole BEM for simulation of 2D elastic solid with large number of inclusions. Acta Mech. Sinica, 20: 613-622, 2004.
- [18] P.B. Wang, Z.H. Yao. Fast multipole DBEM analysis of fatigue crack growth. Comput. Mech., 38: 223-233, 2006.
- [19] P. Wang, Z. Yao, H. Wang. Fast multipole BEM for simulations of 2-D solids containing large number of cracks. Tshingua Science and Technology, 10: 76-81, 2005.
- [20] Z. Yao, F. Kong, H. Wang, P. Wang. 2D simulation of composite materials using BEM. Eng. Anal. Bound. Elem., 28: 927-935, 2004.
- [21] Y. Yamada, K. Hayami. A multipole boundary element method for two dimensional elastostatics, Tech. Rep., METR 95-07, Math. Eng. Section, Dept. Math. Eng., Information Phys., Univ. Tokyo, 1995.
- [22] L. Zhao, Z. Yao. Fast multipole BEM for 3-D elastostatic problems with applications for thin structures. Tshingua Science and Technology, 10: 67-75, 2005.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPB8-0009-0020