Interaction and multiscale mechanics

  • 제3권2호
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  • Pages.123-143
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  • 2010
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  • 1976-0426(pISSN)
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  • 2092-6200(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Improved Element-Free Galerkin method (IEFG) for solving three-dimensional elasticity problems

  • Zhang, Zan (Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University) ;
  • Liew, K.M. (Department of Building and Construction, City University of Hong Kong)
  • 투고 : 2010.03.30
  • 심사 : 2010.05.28
  • 발행 : 2010.06.25
⟨ 이전 논문 다음 논문 ⟩

초록

The essential idea of the element-free Galerkin method (EFG) is that moving least-squares (MLS) approximation are used for the trial and test functions with the variational principle (weak form). By using the weighted orthogonal basis function to construct the MLS interpolants, we derive the formulae for an improved element-free Galerkin (IEFG) method for solving three-dimensional problems in linear elasticity. There are fewer coefficients in improved moving least-squares (IMLS) approximation than in MLS approximation. Also fewer nodes are selected in the entire domain with the IEFG method than is the case with the conventional EFG method. In this paper, we selected a few example problems to demonstrate the applicability of the method.

키워드

참고문헌

  1. Atluri, S.N. and Zhu, T.L. (1998), "A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics", Comput. Mech., 22, 117-127. https://doi.org/10.1007/s004660050346
  2. Belytschko, T., Krongauz, Y., Organ, D., Fleming, M. and Krysl, P. (1996), "Meshless method: an overview and recent developments", Comput. Meth. Appl. Mech. Eng., 139, 3-47. https://doi.org/10.1016/S0045-7825(96)01078-X
  3. Belytschko, T., Lu, Y.Y. and Gu, L. (1994), "Element-free Galerkin methods", Int. J. Numer. Meth. Eng., 37, 229-256. https://doi.org/10.1002/nme.1620370205
  4. Duarte, C.A. and Oden, J.T. (1995), "Hp clouds-a meshless method to solve boundary-value problems", Technical report 95-05, Texas Institute for Computational and Applied Mathematics, University of Texas at Austin.
  5. Hu, H.Y., Lai, C.K. and Chen, J.S. (2009), "A study on convergence and complexity of reproducing kernel collocation method", Interaction Multiscale Mech., 2(3), 295-319. https://doi.org/10.12989/imm.2009.2.3.295
  6. Kitipornchai, S., Liew, K.M. and Cheng, Y. (2005), "A boundary element-free method (BEFM) for threedimensional elasticity problems", Computat. Mech., 36, 13-20. https://doi.org/10.1007/s00466-004-0638-1
  7. Lancaster, P. and Salkauskas, K. (1981), "Surface generated by moving least squares methods", Math. Comput., 37, 141-158. https://doi.org/10.1090/S0025-5718-1981-0616367-1
  8. Liew, K.M, Huang, Y.Q. and Reddy, J.N. (2003), "Moving least-squares differential quadrature method and its application to the analysis of shear deformable plates", Int. J. Numer. Meth. Eng., 56, 2331-2351. https://doi.org/10.1002/nme.646
  9. Liew, K.M. and Chen, X.L. (2004a), "Mesh-free radial basis function method for buckling analysis of nonuniformly loaded arbitrarily shaped shear deformable plates", Comput. Meth. Appl. Mech. Eng., 193, 205-224. https://doi.org/10.1016/j.cma.2003.10.002
  10. Liew, K.M. and Chen, X.L. (2004b), "Mesh-free radial point interpolation method for the buckling analysis of Mindlin plates subjected to in-plane point loads", Int. J. Numer. Meth. Eng., 60, 1861-1877. https://doi.org/10.1002/nme.1027
  11. Liew, K.M. and Chen, X.L. (2004c), "Buckling of rectangular Mindlin plates subjected to partial in-plane edge loads using the radial point interpolation method", Int. J. Solids Struct., 41, 1677-1695. https://doi.org/10.1016/j.ijsolstr.2003.10.022
  12. Liew, K.M., Cheng Yumin, and Kitipornchai, S. (2006), "Boundary element-free method (BEFM) and its application to two-dimensional elasticity problems", Int. J. Numer. Meth. Eng., 65(8), 1310-1332. https://doi.org/10.1002/nme.1489
  13. Liew, K.M., Cheng, Y. and Kitipornchai, S. (2005), "Boundary element-free method (BEFM) for twodimensional elastodynamic analysis using Laplace transform", Int. J. Numer. Meth. Eng., 64, 1610-1627. https://doi.org/10.1002/nme.1417
  14. Liew, K.M., Feng, C., Cheng, Y. and Kitipornchai, S. (2007), "Complex variable moving least-squares method: A meshless approximation technique", Int. J. Numer. Meth. Eng., 70, 46-70. https://doi.org/10.1002/nme.1870
  15. Liew, K.M., Huang, Y.Q. and Reddy, J.N. (2004), "Analysis of general shaped thin plates by the moving leastsquares differential quadrature method", Finite Elem. Anal. Des., 40, 1453-1474. https://doi.org/10.1016/j.finel.2003.10.002
  16. Liu, G.R., Mesh free methods: moving beyond the finite element method, Boca Raton, FL: CRC Press LLC.
  17. Liu, W.K., Jun, S. and Zhang, Y.F. (1995), "Reproducing kernel particle method", Int. J. Numer. Meth. Fl., 20, 1081-1106. https://doi.org/10.1002/fld.1650200824
  18. Matsubara, H. and Yagawa, G. (2009), "Convergence studies for Enriched Free Mesh Method and its application to fracture mechanics", Interaction Multiscale Mech., 2(3), 277-293. https://doi.org/10.12989/imm.2009.2.3.277
  19. Nayroles, B., Touzot, G. and Villon, P.G. (1992), "Generalizing the finite element method: diffuse approximation and diffuse elements", Comput. Mech., 10, 307-318. https://doi.org/10.1007/BF00364252
  20. Sun, Y.Z., Zhang, Z., Kitipornchai, S. and Liew, K.M. (2006), "Analyzing the interaction between collinear interfacial cracks by an efficient boundary element-free method", Int. J. Eng. Sci., 44, 37-48. https://doi.org/10.1016/j.ijengsci.2005.08.005
  21. Wang, D. and Wu, Y. (2008), "An efficient Galerkin meshfree analysis of shear deformable cylindrical panels", Interaction Multiscale Mech., 1(3), 339-355. https://doi.org/10.12989/imm.2008.1.3.339
  22. Wu, C.T. and Koishi, M. (2009), "A Meshfree procedure for the microscopic analysis of particle-reinforced rubber compounds", Interaction Multiscale Mech., 2(2), 129-151. https://doi.org/10.12989/imm.2009.2.2.129

피인용 문헌

  1. A review of meshless methods for laminated and functionally graded plates and shells vol.93, pp.8, 2011, https://doi.org/10.1016/j.compstruct.2011.02.018
  2. Stress state around cylindrical cavities in transversally isotropic rock mass vol.6, pp.3, 2014, https://doi.org/10.12989/gae.2014.6.3.213
  3. The coupling of complex variable-reproducing kernel particle method and finite element method for two-dimensional potential problems vol.3, pp.3, 2010, https://doi.org/10.12989/imm.2010.3.3.277