Structural Engineering and Mechanics

  • 제39권6호
  • /
  • Pages.767-793
  • /
  • 2011
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

An edge-based smoothed finite element method for adaptive analysis

  • Chen, L. (Centre for Advanced Computations in Engineering Science (ACES), National University of Singapore) ;
  • Zhang, J. (Department of Civil and Environmental Engineering, National University of Singapore) ;
  • Zeng, K.Y. (Department of Mechanical Engineering, National University of Singapore) ;
  • Jiao, P.G. (School of Mechanical Engineering, Shandong University)
  • 투고 : 2010.03.03
  • 심사 : 2011.06.22
  • 발행 : 2011.09.25
⟨ 이전 논문 다음 논문 ⟩

초록

An efficient edge-based smoothed finite element method (ES-FEM) has been recently developed for solving solid mechanics problems. The ES-FEM uses triangular elements that can be generated easily for complicated domains. In this paper, the complexity study of the ES-FEM based on triangular elements is conducted in detail, which confirms the ES-FEM produces higher computational efficiency compared to the FEM. Therefore, the ES-FEM offers an excellent platform for adaptive analysis, and this paper presents an efficient adaptive procedure based on the ES-FEM. A smoothing domain based energy (SDE) error estimate is first devised making use of the features of the ES-FEM. The present error estimate differs from the conventional approaches and evaluates error based on smoothing domains used in the ES-FEM. A local refinement technique based on the Delaunay algorithm is then implemented to achieve high efficiency in the mesh refinement. In this refinement technique, each node is assigned a scaling factor to control the local nodal density, and refinement of the neighborhood of a node is accomplished simply by adjusting its scaling factor. Intensive numerical studies, including an actual engineering problem of an automobile part, show that the proposed adaptive procedure is effective and efficient in producing solutions of desired accuracy.

키워드

참고문헌

  1. Anderson, T.L. (1991), Fracture Mechanics: Fundamentals and Applications, 1st Edition, CRC Press, Boca Raton.
  2. 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
  3. Babuska, I. and Rheinboldt, W.C. (1978), "A posteriori error estimates for the finite element method", Int. J. Numer. Meth. Eng., 12, 1597-1615. https://doi.org/10.1002/nme.1620121010
  4. Belytschko, T., Lu, Y.Y. and Gu, L. (1994), "Element free Garlerkin methods", Int. J. Numer. Meth. Eng., 37, 229-256. https://doi.org/10.1002/nme.1620370205
  5. Chen, J.S., Wu, C.T. and Belytschko, T. (2000), "Regularization of material instabilities by meshfree approximations with intrinsic length scales", Int. J. Numer. Meth. Eng., 47, 1303-1322. https://doi.org/10.1002/(SICI)1097-0207(20000310)47:7<1303::AID-NME826>3.0.CO;2-5
  6. Chen, J.S., Wu, C.T., Yoon, S. and You, Y. (2001), "A stabilized conforming nodal integration for Galerkin mesh-free methods", Int. J. Numer. Meth. Eng., 50, 435-466. https://doi.org/10.1002/1097-0207(20010120)50:2<435::AID-NME32>3.0.CO;2-A
  7. Chung, H.J. and Belytschko, T. (1998), "An error estimate in the EFG method", Comput. Mech., 21, 91-100. https://doi.org/10.1007/s004660050286
  8. Choi, C.K. and Chung, H.J. (1995), "An adaptive-control of spatial-temporal discretization error in finite-element analysis of dynamic problems", Struct. Eng. Mech., 3, 391-410. https://doi.org/10.12989/sem.1995.3.4.391
  9. Dohrmann, C.R., Heinstein, M.W., Jung, J., Key, S.W. and Witkowski, W.R. (2000), "Node-based uniform strain elements for three-node triangular and four-node tetrahedral meshes", Int. J. Numer. Meth. Eng., 47, 1549-1568. https://doi.org/10.1002/(SICI)1097-0207(20000330)47:9<1549::AID-NME842>3.0.CO;2-K
  10. Eringen, A.C. and Edelen, D.G.B. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10, 233-248. https://doi.org/10.1016/0020-7225(72)90039-0
  11. Kee, B.B.T., Liu, G.R. and Zhang, G.Y. (2008), "A residual based error estimator using radial basis functions", Finite Elem. Anal. Des., 44, 631-645. https://doi.org/10.1016/j.finel.2008.02.002
  12. Lee, C., Im, C.H. and Jung, H.K. (1998), "A posteriori error estimation and adaptive node refinement for fast moving least square reproducing kernel (FMLSRK) method", CMES: Comp. Model. Eng. Sci., 20, 35-41.
  13. Liu G.R. (2002), Mesh Free Methods: Moving Beyond the Finite Element Method, CRC Press, Boca Raton.
  14. Liu, G.R. (2008), "A generalized gradient smoothing technique and the smoothed bilinear form for Galerkin formula of a wide class of computational methods", Int. J. Comput. Meth., 5, 199-236. https://doi.org/10.1142/S0219876208001510
  15. Liu, G.R., Dai, K.Y. and Nguyen, T.T. (2007), "A smoothed finite element method for mechanics problems", Comput. Mech., 39, 859-877. https://doi.org/10.1007/s00466-006-0075-4
  16. Liu, G.R., Nguyen, T.T. and Dai, K.Y. (2007), "Theoretical aspects of the smoothed finite element method (SFEM)", Int. J. Numer. Meth. Eng., 71, 902-930. https://doi.org/10.1002/nme.1968
  17. Liu, G.R., Nguyen-Thoi, T. and Lam, K.Y. (2008), "An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analysis", J. Sound Vib., 320, 1100-1130.
  18. Liu, G.R., Nguyen-Thoi, T. and Lam, K.Y. (2009), "A node-based smoothed finite element method for upper bound solution to solid problems (NS-FEM)", Comput. Struct., 87, 14-26. https://doi.org/10.1016/j.compstruc.2008.09.003
  19. Liu, G.R., Nguyen-Thoi, T., Nguyen-Xuan, H., Dai, K.Y. and Lam, K.Y. (2009), "On the essence and the evaluation of the shape functions for the smoothed finite element method (SFEM)", Int. J. Numer. Meth. Eng., 77, 1863-1869. https://doi.org/10.1002/nme.2587
  20. Liu, G.R. and Quek, S.S. (2003), The Finite Element Method: A Practical Course, Butterworth Heinemann, Oxford.
  21. Liu, G.R. and Tu, Z.H. (2002), "An adaptive procedure based on background cells for Meshfree methods", Comput. Meth. Appl. Mech. Eng., 191, 1923-1943. https://doi.org/10.1016/S0045-7825(01)00360-7
  22. Liu, G.R. and Zhang, G.Y. (2005), "A linearly conforming point interpolation method (LC-PIM) for 2D solid mechanics problems", Int. J. Comput. Meth., 2, 645-665. https://doi.org/10.1142/S0219876205000661
  23. Lucy, L.B. (1977), "Numerical approach to testing the fission hypothesis", Astrono. J., 82, 1013-1024. https://doi.org/10.1086/112164
  24. Nguyen-Thoi, T., Liu, G.R. and Lam, K.Y. (2009), "A face-based smoothed finite element method (FS-FEM) for 3D linear and nonlinear solid mechanics problems using 4-node tetrahedral elements", Int. J. Numer. Meth. Eng., 78, 324-353. https://doi.org/10.1002/nme.2491
  25. Ozakca, M. (2003), "Comparison of error estimation methods and adaptivity for plane stress/strain problems", Struct. Eng. Mech., 15, 579-608. https://doi.org/10.12989/sem.2003.15.5.579
  26. Timoshenko, S.P. and Goodier, J.N. (1977), Theory of Elasticity, McGraw-Hill, New York.
  27. Yoo, J., Moran, W.B. and Chen, J.S. (2004), "Stabilized conforming nodal integration in the natural-element method", Int. J. Numer. Meth. Eng., 60, 861-890. https://doi.org/10.1002/nme.972
  28. Zhang, G.Y. and Liu, G.R. (2008), "An efficient adaptive analysis procedure for certified solutions with exact bounds of strain energy for elastic problems", Finite Elem. Anal. Des., 44, 831-841. https://doi.org/10.1016/j.finel.2008.06.010
  29. Zhang, J., Liu, G.R., Lam, K.Y., Li, H. and Xu, G. (2008), "A gradient smoothing method (GSM) based on strong form governing equation for adaptive analysis of solid mechanics problems", Finite Elem. Anal. Des., 44, 889-909. https://doi.org/10.1016/j.finel.2008.06.006
  30. Zienkiewicz, O.C. and Taylor, R.L. (2000), The Finite Element Method, 5th Edition, Butterworth Heinemann, Oxford.
  31. Zienkiewicz, O.C. and Zhu, J.Z. (1987), "A simple error estimator and adaptive procedure for practical engineering analysis", Int. J. Numer. Meth. Eng., 24, 337-357. https://doi.org/10.1002/nme.1620240206

피인용 문헌

  1. Investigating the Effect of Several Model Configurations on the Transient Response of Gas-Insulated Substation during Fault Events Using an Electromagnetic Field Theory Approach vol.13, pp.23, 2020, https://doi.org/10.3390/en13236231