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The Method of Fundamental Solutions applied to 3D structures with body forces using particular solutions

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Abstract

This paper presents the Method of Fundamental Solutions for three-dimensional elastostatics with body forces. The gravitational body loading is considered as an example for the treated body forces. A new set of particular solutions corresponding to such loading is derived using Hörmander operator-decoupling technique, and the relevant particular solution expressions for displacements, tractions and stresses are derived and given explicitly. Several examples are tested and the results confirm the validity and efficiency of the presented method.

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References

  • Zeinkiewicz OC (1977) The Finite Element Method, 3rd Edition. McGraw-Hill, UK

  • Brebbia CA, Dominguez J (1992) Boundary Elements an Introductory Course, Computational Mechanics publications, McGraw-Hill

  • BEASY User Manual (1998) Computational Mechanics publications

  • Popov V, Power H (2001) An O(N) Taylor series multipole boundary element method for three dimensional elasticity problems. Engng Anal Boundary Elements 25:7–18

    Google Scholar 

  • Crouch SL, Starfield AM (1983) Boundary Element Methods in Solid Mechanics. George Allen & Unwin (Publishers) Ltd

  • Brebbia CA, Butterfield R (1978) Formal equivalence of direct and indirect boundary element methods. Appl Math Modeling Vol. 2

  • Fam GSA, Rashed YF (2002) A Study on the Source Points Locations in the Method of Fundamental Solutions. Proceeding of Boundary Elements XXIV, WIT Press

  • Murashima S, Nonaka Y, Nieda H (1983) The Charge Simulation Method and its Application to Two-dimensional Elasticity. Proceeding of Boundary Elements V, Springer-Verlag

  • Patterson C, Sheikh MA (1983) A Modified Trefftz Method for Three-Dimensional Elasticity. Proceedings of the fifth International Conference BEM V, Hiroshima, Japan

  • Burguess G, Mahajerin E (1987) The fundamental collocation method applied to the nonlinear poisson equation in two dimensions. Comput Struct 27(6)

  • Wearing JL, Sheikh MA (1988) Three Dimensional Stress Analysis using an Indirect Discrete Boundary Method. (ed), Proceedings of the first European Boundary Element Meeting, Brussels, In: Migeot JL Univ. Libre de Bruxelles

  • Patterson C, Sheikh MA, Scholfield RP (1985) On the Application of the Indirect Discrete Method for Three-dimensional Design Problem. BETECH 85, Springer Verlag

  • Chen CS (1995) Method of fundamental solutions for non-linear thermal explosions. Commun Numer Meth Eng 11:675–681

    Google Scholar 

  • Karageorghis A, Fairweather G (1987) The method of fundamental solutions for the numerical solution of the biharmonic equation. J Comput Phys, 69:434–459

    Google Scholar 

  • Partridge PW, Sensale B (2000) The method of fundamental solutions with dual reciprocity for diffusion and diffusion-convection using subdomains. Eng Anal Boundary Elem 24

  • Patterson C, Sheikh MA (1982) On The Use of Fundamental Solutions in Trefftz Method for Potential and Elasticity problems. Proceedings of the fourth International Conference BEM IV, Springer Verlag, Hiroshima, Japan

  • Redekop D (1982) Fundamental solutions for the collocation method in planar elastostatics. Appl Math Model Vol. 6

  • Karageorghis A, Fairweather G (2000) The method of fundamental solutions for axisymmetric elasticity problems. Comput Mech 25

  • Redekop D, Thompson JC (1983) Use of fundamental solutions in the collocation method in axisymetric elastostatics. Comput Struct 17(4):485–490

    Google Scholar 

  • Redekop D, Cheung RSW (1987) Fundamental solutions for the collocation method for three-dimensional elastostatics. Comput struct 26(4)

  • Poullikas A, Karageorghis A, Georgiou G (2002) The method of fundamental solutions for three-dimensional elastostatics problems. Comput Struct 80:365–370

    Google Scholar 

  • Koopmann GH, Song L, Fahnline JB (1989) A method for computing acoustic fields based on the principle of wave superposition. J Acoust Soc Am 86(6) Acoustical Society of America

  • Alves CJS, Chen CS, Saler B (2002) The Method of Fundamental Solutions for Solving Poisson Problems. Proceeding of Boundary Elements XXIV, WIT Press

  • Golberg MA, Chen CS, Moleshkov AS (1999) The Method of Fundamental Solutions for Time Dependant Problems. Boundary Element Technology XIII, WIT Press

  • Belytschko T, Lu YY, Gu L (1994) Element-free galerkin method. Int J Numer Meth Eng 27:229–256

    Google Scholar 

  • Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P (1996) Meshless methods: An overview and recent developments. Comput Meth Appl Mech Engrg 139:3–47

    Google Scholar 

  • Li J, Chen CS, Pepper D, Chen Y (2002) Mesh-free method for groundwater modeling. In: Boundary Elements XXIV, Brebbia CA, Tadeu A, Popov V, (eds) WIT Press, Southampton, Boston, pp. 115–124

  • Kita E, Kamiya N (1995), Trefftz method, an overview. Adv Eng software, 24:3–12

    Google Scholar 

  • Chen W (2002) Meshfree boundary particle method applied to Helmholtz problems. Eng Anal Boundary Elem 26(7):577–581

    Google Scholar 

  • Atluri SN, Kim H-G, Cho JY (1999) A Critical Assessment of the Truly Meshless Local Petrov-Galerkin (MLPG), and Local Boundary Integral Equation (LBIE) methods. Computational Mechanics. Volume 24, Issue 5, Springer-Verlag, Berlin, pp. 348–372

  • Rashed YF, Brebbia CA (eds) (2003) Transformation of Domain Effects to the Boundary. WIT Press

  • De Mederios GC, Partridge PW (2003) The Method of Fundamental Solutions with Dual Reciprocity for Thermoelasticity. International workshop on meshfree methods

  • Pape DA, Banerjee PK (1987) Treatment of body forces in 2D elastostatic BEM using particular integrals. J Appl Mech, ASME

  • Timoshenko SP, Goodier JN (1970) Theory of Elasticity. 3rd Edition. McGraw-Hill

  • Rashed YF (2002) Boundary Element Primer-Tutorial 4. Boundary Element Communications, Vol. 13, NO 1, WIT Press, 2002.

  • Rashed, YF (2002) Boundary Element Primer - Tutorial 5. Boundary Element Communications, Vol. 13, NO 2, WIT Press

  • Hörmander L (1963) Linear Partial Differential Operators. Springer-Verlag, Berlin

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Authors and Affiliations

  1. Wessex Institute of Technology, Southampton, SO40 7AA, UK

    George S. A. Fam

  2. Dept. of Structural Engineering, Cairo University, Giza, Egypt

    Youssef F. Rashed

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  1. George S. A. Fam
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  2. Youssef F. Rashed
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Correspondence to Youssef F. Rashed.

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Fam, G., Rashed, Y. The Method of Fundamental Solutions applied to 3D structures with body forces using particular solutions. Comput Mech 36, 245–254 (2005). https://doi.org/10.1007/s00466-004-0661-2

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