Structural Engineering and Mechanics

  • 제48권6호
  • /
  • Pages.775-789
  • /
  • 2013
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

A novel 3D BE formulation for general multi-zone domains under body force loading

  • Ghiasian, Mohammad (Department of Civil and Environmental Engineering, Tarbiat Modares University) ;
  • Ahmadi, Mohammad Taghi (Department of Civil and Environmental Engineering, Tarbiat Modares University)
  • 투고 : 2013.05.08
  • 심사 : 2013.11.09
  • 발행 : 2013.12.25
⟨ 이전 논문 다음 논문 ⟩

초록

The current paper proposes a boundary element formulation, applicable to 2-D and 3-D elastostatics problems using a unified approach for transformations of the domain integrals into boundary integrals. The method is applicable to linear problems encompassing both finite and infinite multi-region domains allowing non-vanishing body forces. Numerical results agree quite well with the analytical solutions; while the present method offers easy formulation with less numerical efforts in comparison to FEM or some BEM which need interior points to treat arbitrary body forces. It is demonstrated that the method has the potential to have profound impact on engineering design, notably in dam-foundation interaction.

키워드

참고문헌

  1. Ahmadi, M.T., Izadinia, M and Bachmann, H. (2001), "A discrete crack joint model for nonlinear dynamic analysis of concrete arcli dam", Int. J. Comput. Struct, 79, 403-420. https://doi.org/10.1016/S0045-7949(00)00148-6
  2. Aliabadi, M.H. (2002), The Boundary Element Method, John Wiley & Sons, London, UK.
  3. Banerjee, P.K. (1994), The Boundary Element Methods in Engineering, McGraw-Hill Book Company, London, UK.
  4. Beer, G. (1993), "An efficient numerical metliod for modelling initiation and propagation of cracks along material interfaces", Internationa Journal for Numerical Methods in Engineering, 36, 3579-3594. https://doi.org/10.1002/nme.1620362102
  5. Beer, G. and Poulsen, B.A (1994), "Efficient numerical modeling of faulted rock using tlie boundary element metliod", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 31(5), 485-506. https://doi.org/10.1016/0148-9062(94)90151-1
  6. Beer, G., Smith, I. and Duenser, C. (2008), The Boundary Element Method With Programming, Springer-Verlag, Wien, Germany.
  7. Brebbia, A, Talles, J.C.F and Wrobel, L.C. (1984), Boundary Element Techniques, Springer-Verlog, New York, USA
  8. Clieng, S. and Shuwei, Z. (2012), "Stocliastic spline fictitious boundary element method in elastostatic problems with random fields", Eng. Anal. Bound Elem., 36(5), 759-771. https://doi.org/10.1016/j.enganabound.2011.11.014
  9. Deb, A. and Banerjee, P.K. (1990), "BEM for general anisotropic 2D elasticity using particular integrals", Commun. Appl. Numer. Method., 6, 111-119. https://doi.org/10.1002/cnm.1630060207
  10. Federal Energy Regulation Commission (1999), Chapter 11: Arch Dams, Engineering Guidelines for the Evaluation of Hydropower Projects, Washington D. C, USA.
  11. Federal Energy Regulation Commission (1991), Chapter 5: Geotechnical Investigations and Studies, Engineering Guidelines for the Evaluation of Hydropower Projects, Washington D.C., USA.
  12. Khodakarami, M.I. and Kaji, N. (2011), "Analysis of elastostatics problems using a semi-analytical method with diagonal coefficient matrices", Eng Anal. Bound. Elem., 35, 1288-1296. https://doi.org/10.1016/j.enganabound.2011.06.003
  13. Kuo, H.Y. and Chen, T. (2005), "Steady and transient Green's functions for anisotropic conduction in an exponentially graded solid", Int. J. Solid Struct, 42, 1111-1128. https://doi.org/10.1016/j.ijsolstr.2004.06.060
  14. Leonel, E.D. and Wilson, S.V. (2011), "Non-linear boundary element formulation applied to contact analysis using tangent operator", Eng. Anal. Bound. Elem., 35, 1237-1247. https://doi.org/10.1016/j.enganabound.2011.06.005
  15. Leonel, E.D. and Wilson, S.V. (2010a), "Dual boundary element formulation applied to analysis of multifractured domains", Eng Anal. Bound Elem., 34(12), 1092-1099. https://doi.org/10.1016/j.enganabound.2010.06.014
  16. Leonel, E.D. and Wilson, S.V. (2010b), "Non-linear boundary element formulation with tangent operator to analyse crack propagation", Eng Anal. Bound. Elem., 34, 122-129. https://doi.org/10.1016/j.enganabound.2009.08.005
  17. Maerten, F. (2010), "Adaptive cross-approximation applied to the solution of system of equations and postprocessing for 3D elastostatic problems using the boundary element method", Eng Anal. Bound. Elem., 34(5),483-491. https://doi.org/10.1016/j.enganabound.2009.10.016
  18. Milroy, J., Hinduja, S. and Davey, K. (1997), "The elastostatics three-dimensional boundary element method: analytical integration for linear isoparametric triangular elements", Appl. Math. Model., 21, 763-782. https://doi.org/10.1016/S0307-904X(97)00098-X
  19. Ochiai, Y. and Kobayashi, T. (2000), "Stress analysis with arbitrary body force by triple-reciprocity BEM" Struct. Eng. Mech., 10(4), 393-404. https://doi.org/10.12989/sem.2000.10.4.393
  20. Park, K.H. (2002), "A BEM formulation for axisymmetric elasticity with arbitrary body force using particular integrals", Int. J. Comput. Struct., 80, 2507-2514. https://doi.org/10.1016/S0045-7949(02)00346-2
  21. Park, K.H. and Banerjee, P.K. (2002), "Two- and three-dimensional transient thermoelastic analysis by BEM via particular integrals", Int. J. Solid. Struct., 39, 2871-2892. https://doi.org/10.1016/S0020-7683(02)00125-7
  22. Pereira, A. and Beer, G. (2009), "Interface dynamic stiffness matrix approach for three-dimensional transient multi-region boundary element analysis", Int. J. Numer. Method. Eng., 80, 1463-1495. https://doi.org/10.1002/nme.2680
  23. Perez-Gavilan, J.J. and Aliabadi, M.H. (2001), "A symmetric galerkin formulation and dual reciprocity for 2D elastostatics", Eng Anal. Bound. Elem., 25, 229-235. https://doi.org/10.1016/S0955-7997(01)00003-0
  24. Rodriguez-Tembleque, L. and Abascal, R. (2010) "A 3D FEM-BEM rolling contact formulation for unstructured meshes", Int. J. Solid. Struct., 47, 330-353. https://doi.org/10.1016/j.ijsolstr.2009.10.008
  25. Shen, S.Y. (2011), "An indirect elastostatics boundary element method with analytic bases", Int. J. Comput Struct., 89, 2402-2413. https://doi.org/10.1016/j.compstruc.2011.06.008
  26. Simpson, R.N., Bordas, S.P.A., Lian, H. and Trevelyan, J. (2013), "An isogeometric boundary element method for elastostatics analysis: 2D implementation aspects", Int J. Comput. Struct., 118, 2-12. https://doi.org/10.1016/j.compstruc.2012.12.021
  27. Tang, W.C. and Fenner, R.T. (2005), "Analytical integration and exact geometrical representation in the two-dimensional elastostatics boundary element method", Appl. Math. Model. 29, 1073-1099. https://doi.org/10.1016/j.apm.2005.02.011
  28. Timoshenko, S.P. and Goodier, J.N. (1970), Theory Of Elasticity, 3rd Edition, McGraw-Hill, New York, USA.

피인용 문헌

  1. Efficient 3D boundary element dynamic analysis of discontinuities vol.50, 2015, https://doi.org/10.1016/j.enganabound.2014.09.006