Interaction and multiscale mechanics

  • 제3권3호
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  • Pages.277-298
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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

The coupling of complex variable-reproducing kernel particle method and finite element method for two-dimensional potential problems

  • Chen, Li (Department of Building and Construction, City University of Hong Kong) ;
  • Liew, K.M. (Department of Building and Construction, City University of Hong Kong) ;
  • Cheng, Yumin (Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University)
  • 투고 : 2010.07.07
  • 심사 : 2010.09.21
  • 발행 : 2010.09.25
⟨ 이전 논문 다음 논문 ⟩

초록

The complex variable reproducing kernel particle method (CVRKPM) and the FEM are coupled in this paper to analyze the two-dimensional potential problems. The coupled method not only conveniently imposes the essential boundary conditions, but also exploits the advantages of the individual methods while avoiding their disadvantages, resulting in improved computational efficiency. A hybrid approximation function is applied to combine the CVRKPM with the FEM. Formulations of the coupled method are presented in detail. Three numerical examples of the two-dimensional potential problems are presented to demonstrate the effectiveness of the new method.

키워드

참고문헌

  1. Aluru, N.R. (2000), "A point collocation method based on reproducing kernel approximations", Comput. Method. Appl. M., 47, 1083-1121.
  2. Atluri, S.N. and Zhu, T.L. (1998), "A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics", Computat. Mech., 22, 117-127. https://doi.org/10.1007/s004660050346
  3. Belytschko, T. and Organ, D. (1995), "Coupled finite element-element-free Galerkin method", Computat. Mech., 17, 186-195. https://doi.org/10.1007/BF00364080
  4. Belytschko, T., Krongauz, Y., Organ, D., Fleming, M. and Krysl, P. (1996), "Meshless method: an overview and recent developments", Comput. Method. Appl. M., 139, 3-47. https://doi.org/10.1016/S0045-7825(96)01078-X
  5. Belytschko, T., Lu, Y.Y. and Gu, L. (1994), "Element-free Galerkin methods", Int. J. Numer. Method. Eng., 37, 229-256. https://doi.org/10.1002/nme.1620370205
  6. Chen, J.S., Chen, C., Wu, C.T. and Liu, W.K. (1996), "Reproducing kernel particle methods for large deformation analysis of nonlinear structures", Comput. Method. Appl. M., 139, 195-229. https://doi.org/10.1016/S0045-7825(96)01083-3
  7. Chen, L. and Cheng, Y. (2008a), "Reproducing kernel particle method with complex variables for elasticity", Acta Physica Sinica, 57, 1-10 (in Chinese).
  8. Chen, L. and Cheng, Y. (2008b), "Reproducing kernel particle method with complex variables for transient heat conduction problems", Acta Physica Sinica, 57, 6047-6055 (in Chinese).
  9. Dolbow, J. and Belytschko, T. (1999), "Volumetric locking in the element free Galerkin method", Int. J. Numer. Meth. Eng., 46, 925-942. https://doi.org/10.1002/(SICI)1097-0207(19991030)46:6<925::AID-NME729>3.0.CO;2-Y
  10. Gu, T.Y. and Liu, G.R. (2005), "Meshless methods coupled with other numerical method", Tsinghua Sci. Technol., 10, 8-15. https://doi.org/10.1016/S1007-0214(05)70003-1
  11. Hu, H.Y., Lai, C.K. and Chen, J.S., (2009), "A study on convergence and complexity of reproducing kernel collocation method", Interact. Multiscale Mech., 2(3), 295-319. https://doi.org/10.12989/imm.2009.2.3.295
  12. Kothnur, V.S., Mukherjee, S. and Mukherjee, Y.X. (1999), "Two dimensional linear elasticity by the boundary node method", Int. J. Solids Struct., 36, 1129-1147. https://doi.org/10.1016/S0020-7683(97)00363-6
  13. 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. Method. Appl. M., 193, 205-224. https://doi.org/10.1016/j.cma.2003.10.002
  14. 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
  15. Liew, K.M. and Cheng, Y. (2009), "Complex variable boundary element-free method for two-dimensional elastodynamic problems", Comput. Method. Appl. M., 198, 3925-3933. https://doi.org/10.1016/j.cma.2009.08.020
  16. Liew, K.M. and Huang, Y.Q. (2003), "Bending and buckling of thick symmetric rectangular laminates using the moving least-squares differential quadrature method", Int. J. Mech. Sci., 45, 95-114. https://doi.org/10.1016/S0020-7403(03)00037-7
  17. 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
  18. Liew, K.M., Cheng, Y. and Kitipornchai, S. (2006), "Boundary element-free method (BEFM) and its application to two-dimensional elasticity problems", Int. J. Numer. Meth. Eng., 65, 1310-1332. https://doi.org/10.1002/nme.1489
  19. 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
  20. 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
  21. 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
  22. 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, 1453-74. https://doi.org/10.1016/j.finel.2003.10.002
  23. Liew, K.M., Ng, T.Y. and Wu, Y.C. (2002a), "Meshfree method for large deformation analysis - a reproducing kernel particle approach", Eng. Struct., 24, 543-551. https://doi.org/10.1016/S0141-0296(01)00120-1
  24. Liew, K.M., Ng, T.Y., Zhao, X. and Reddy, J.N. (2002), "Harmonic reproducing kernel particle method for free vibration analysis of rotating cylindrical shells", Comput. Method. Appl. M., 191, 4141-4157. https://doi.org/10.1016/S0045-7825(02)00358-4
  25. Liew, K.M., Wang, J., Tan, M.J. and Rajendran, S. (2004), "Nonlinear analysis of laminated composite plates using the mesh-free kp-Ritz method based on FSDT", Comput. Method. Appl. M., 193, 4763-4779. https://doi.org/10.1016/j.cma.2004.03.013
  26. Liew, K.M., Wu, Y.C., Zou, G.P. and Ng, T.Y. (2002b), "Elasto-plasticity revisited: Numerical analysis via reproducing kernel particle method and parametric quadratic programming", Int. J. Numer. Meth. Eng., 55, 669-683. https://doi.org/10.1002/nme.523
  27. Liu, W.K. and Chen, Y.J. (1995), "Wavelet and multiple scale reproducing kernel methods", Int. J. Numer. Meth. Fl., 21, 901-931. https://doi.org/10.1002/fld.1650211010
  28. Liu, W.K. and Jun, S. (1998), "Multiple-scale reproducing kernel particle methods for large deformation problems", Int. J. Numer. Meth. Eng., 41, 1339-1362. https://doi.org/10.1002/(SICI)1097-0207(19980415)41:7<1339::AID-NME343>3.0.CO;2-9
  29. Liu, W.K., Chen, Y., Jun, S., Chen, J.S. and Belytschko, T. (1996), "Overview and applications of the reproducing kernel particle methods", Archives of Computer Methods in Engineering, State of the Art Review 3, 3-80. https://doi.org/10.1007/BF02736130
  30. Liu, W.K., Jun, S. and Zhang, Y.F. (1995), "Reproducing kernel particle methods", Int. J. Numer. Meth. Fl., 20, 1081-1106. https://doi.org/10.1002/fld.1650200824
  31. Liu, W.K., Jun, S., Li, S., Adee, J. and Belytschko, T. (1995), "Reproducing kernel particle methods for structural dynamics", Int. J. Numer. Meth. Eng., 38, 1655-1679. https://doi.org/10.1002/nme.1620381005
  32. Liu, W.K., Jun, S., Thomas, S.D., Chen, Y. and Hao, W. (1997), "Multiresolution reproducing kernel particle method for computational fluid mechanics", Int. J. Numer. Meth. Fl., 24, 1391-1415. https://doi.org/10.1002/(SICI)1097-0363(199706)24:12<1391::AID-FLD566>3.0.CO;2-2
  33. Liu, Y., Liew, K.M., Hon, Y.C. and Zhang, X. (2005), "Numerical simulation and analysis of an electroactuated beam using a radial basis function", Smart Mater. Struct., 14, 1163-1171. https://doi.org/10.1088/0964-1726/14/6/009
  34. Onarte, E. (1996), "A finite point method in computational mechanics", Int. J. Numer. Meth. Eng., 39, 3839- 3866. https://doi.org/10.1002/(SICI)1097-0207(19961130)39:22<3839::AID-NME27>3.0.CO;2-R
  35. Selvadurai, A.P.S. (2000) Partial differential equations in mechanics 1, Berlin, Heidelberg: Springer.
  36. 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
  37. Zhang, Z. and Liew, K.M. (2010), "Improved element-free Galerkin method (IEFG) for solving three dimensional elasticity problems", Interact. Multiscale Mech., 3, 123-143. https://doi.org/10.12989/imm.2010.3.2.123
  38. Zhao, X., Ng, T.Y. and Liew, K.M. (2004), "Free vibration of two-side simply-supported laminated cylindrical panels via the mesh-free kp-Ritz method", Int. J. Mech. Sci., 46, 123-142. https://doi.org/10.1016/j.ijmecsci.2004.02.010
  39. Zhao, X., Yang, Y. and Liew, K.M. (2007), "Geometrically nonlinear analysis of cylindrical shells using the element-free kp-Ritz method", Eng. Anal. Bound. Elem., 31, 783-792. https://doi.org/10.1016/j.enganabound.2007.01.003
  40. Zhu, T., Zhang, J.D. and Atluri, S.N. (1998), "A local boundary integral equation (LBIE) method in computational mechanics and a meshless discretization approach", Computat. Mech., 21, 223-235. https://doi.org/10.1007/s004660050297

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  6. Numerical solution of potential problems using radial basis reproducing kernel particle method vol.13, pp.None, 2010, https://doi.org/10.1016/j.rinp.2019.02.058