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Trefftz radial basis functions (TRBF)

Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The TRBF's are radial functions satisfying governing equation in the domain. They can be used as interpolation functions of the field variables especially in boundary methods. In present paper discrete dipoles are used to simulate composite material reinforced by stiff particles using with boundary point collocation method which does not require any meshing and any integration. The better the interpolation (unction satisfies also the boundary conditions, the more efficient it is. In examples it is shown that a triple dipole (which is a TRBK) located into the center of the particle can approximate the inter-domain boundary conditions very good, if the particles are not very close to each other and their size is not very different. In general problem the model can be used as very good start point for international improvements in refined model. (Composite reinforced by short fibres with very large aspect ratio continuous TRBF were developed. They enable to reduce problem considerably and to simulate complicated interactions for investigation such composites.
Rocznik
Strony
239--249
Opis fizyczny
Bibliogr. 29 poz., tab., wykr.
Twórcy
autor
autor
  • Academy of Armed Forces of general M. R. Stefanik, Liptovsky Mikulas, Slovakia
Bibliografia
  • [1] V.I. Blokh. Theory of Elasticity. University Press, Kharkov, 1964.
  • [2] J.D. Eshelby. Elastic inclusions and inhomogeneities. In: N.I. Sneddon, R. Hill, eds., Progress in Solid Mechanic, Vol. 2. North-Holland, 1961.
  • [3] C. Filip, B. Garnier, F. Danes. Prediction of the effective thermal conductivity of composites with spherical particles of higher thermal conductivity than the one of the polymer matrix. Proc. of COMSOL Multiphysics User's Conference, Paris, 2005.
  • [4] Y. Fu, K.J. Klimkowski, G.J. Rodin. A fast solution method for three-dimensional many-particle problems in linear elasticity. Int. J. Numer. Meth. Engrg., 42(7): 1215-1229, 1998,
  • [5] M.A. Golberg, C.S. Chen. The method of fundamental solutions for potential, Helmholtz and diffusion problems. Boundary Integral Methods - Numerical and Mathematical Aspects, 1(1): 103-176, WIT Press, 1998.
  • [6] J.E. Gomez, H. Power. A multipole direct and indirect BEM for 2D cavity flow at low Reynolds number. Eng. Anal. Boundary Elem., 19(1): 17-31, 1997.
  • [7] F.L. Greengard, V. Rokhlin. A fast algorithm for particle simulations, J. Comput. Phys., 73(2) 325 348. 1987.
  • [8] Z. Hashin, S. Shtrikman. A variational approach to the theory of the elastic behaviour of multiphase materials J. Mech. Phys. Solids, 11: 127-140, 1963.
  • [9] J. Jirousek. Basis for the development of large finite elements locally satisfying all field equations. Comp. Meth. Appl. Mech. Eng., 14(1): 65-92, 1978.
  • [10] M. Kachanov, B. Shafiro, I. Tsukrov. Handbook of Elasticity Solutions. Kluwer Academic Publishers, Dordrecht, 2003.
  • [11] A. Karageorghis, G. Fairweather. The method of fundamental solutions for the solution of nonlinear plane potential problems. IMA J. Num. Anal, 9(2): Oxford University Press, 231-242, 1989.
  • [12] V. Kompis. M. Stiavnicky, M. Kompis, M. Zmindak. Trefftz interpolation based multi-domain boundary point method. Engrg. Anal. Boundary Elem., 29: 391-396, 2005.
  • [13] V. Kompis, M. Stiavnicky, M. Kompis, Z. Murcinkova, Q.-H. Qin. Method of continuous source functions for modeling of matrix reinforced by finite fibres. In: V. Kompis, ed., Composites with Micro- and Nano-Structure Springer, pp. 27-45, 2007.
  • [14] V. Kompiš, M. Stiavnicky, Q.-H. Qin. Efficient solution for composites reinforced by particles. To be published in Recent Advances in BEM, book to honor Prof. D.E. Beskos.
  • [15] Y.L. 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. ASME J. Appl. Mech., 72: 115-128, 2005.
  • [16] A.A. Mammoli, M.S. Ingber. Stokes flow around cylinders in a bounded two-dimensional domain using multipotaH accelerated boundary element method. Int. J. Numer. Meth. Engrg., 44(7): 897-917, 1999.
  • [17] T. Mori, K. Tanaka. Average stressing matrix and average elastic energy of materials with misfitting inclusion^B Acta Metall., 21: 571-574, 1973.
  • [18] N. Nishimura. Fast multipole accelerated boundary integral equations. Appl. Mech. Rev., 55(4): 299-324, 2002.
  • [19] N. Nishiniura. Y.I.. Liu. Thermal analysis of carbon-nanotube composites using a rigid-line inclusion model by boundary integral equation method, Comput. Mech., 35: 1-10, 2004.
  • [20] Nishiniura, K. Yoshida, S. Kobayashi. A fast multipole boundary integral equation method for crack problems ), Engrg. Anal. Boundary Elem.. 23(1): 97-105, 1999.
  • [21] A. P. Pierce. J.A.L. Napier. A spectral multipole method for efficient solution of large-scale boundary element models in elastostatics, Int. Journ. Numer. Meth. Eng., 38(23): 4009-4034, 1995.
  • [22] J Qu, M. Cherkaoui. Fundamentals of Micromechanics of Solids. Wiley, Hoboken, New Jersey, 2006.
  • [23] S. Rjasanow. Fast and accurate boundary element method. Proc. APCOM'07-EPMESC XI, 2007, Kyoto, CD-ROM. 2007.
  • [24] Shen, Y..I. Liu. An adaptive fast multipole boundary element method for three-dimensional potential problems. Comput. Mech, 39: 681-691, 2007.
  • [25] R.A. Sauer. G. Wang. S. Li. The composite Eshelby tensors and their application to homogenization. Acta Mech.(to be published).
  • [26] E. Trefftz. Ein Gegenstiick zum Ritzschen Verfahren. Proceedings 2nd International Congress of Applied Mechanics, Zurich, pp. 131 137, 1926.
  • [27] H. Wang, Q.H. Qin, Y.L. Kang. A new meshless method for steady-state heat conduction in anisotropic problems and inhomogencous media. Arch. Appl. Mechanics, 74(8): 563-579, 2005.
  • [28] Q.H. Qin, Y.L. Kang. A meshless model for transient heat conduction in functionally graded materials. it Mech., 38(1): 51-60, 2006.
  • [29] H Wang, Q.H. Qin. A meshless method for generalized linear and nonlinear Poisson-type problems, Engrg. Anal.Boundary Elem., 30(6): 515-521, 2006.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPB2-0046-0002
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