Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Meshless formulation for shear-locking free bending elements

  • Kanok-Nukulchai, W. (School of Civil Engineering, Asian Institute of Technology) ;
  • Barry, W.J. (School of Civil Engineering, Asian Institute of Technology) ;
  • Saran-Yasoontorn, K. (School of Civil Engineering, Asian Institute of Technology)
  • Published : 2001.02.25
⟨ Previous Next ⟩

Abstract

An improved version of the Element-free Galerkin method (EFGM) is presented here for addressing the problem of transverse shear locking in shear-deformable beams with a high length over thickness ratio. Based upon Timoshenko's theory of thick beams, it has been recognized that shear locking will be completely eliminated if the rotation field is constructed to match the field of slope, given by the first derivative of displacement. This criterion is applied directly to the most commonly implemented version of EFGM. However in the numerical process to integrate strain energy, the second derivative of the standard Moving Least Square (MLS) shape functions must be evaluated, thus requiring at least a $C^1$ continuity of MLS shape functions instead of $C^0$ continuity in the conventional EFGM. Yet this hindrance is overcome effortlessly by only using at least a $C^1$ weight function. One-dimensional quartic spline weight function with $C^2$ continuity is therefore adopted for this purpose. Various numerical results in this work indicate that the modified version of the EFGM does not exhibit transverse shear locking, reduces stress oscillations, produces fast convergence, and provides a surprisingly high degree of accuracy even with coarse domain discretizations.

Keywords

References

  1. 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
  2. Belytschko, T., Krongauz, Y., Organ, D., Fleming, M. and Krysl, P. (1996), "Meshless methods: An overview and recent developments", Comput. Meth. Appl. Mech. Eng., 113, 397-414.
  3. Cook, R.D., Malkus, D.S. and Plesha, M.E., (1989), Concepts and Applications of Finite Element Analysis, 3rd Edn., John Wiley & Sons, New York.
  4. Donning, B.M. and Liu, W.K. (1998), "Meshless methods for shear-deformable beams and plates", Comput. Meth. Appl. Mech. Eng., 152, 47-72. https://doi.org/10.1016/S0045-7825(97)00181-3
  5. Hughes, T.J.R., Taylor, R.L. and Kanok-Nukulchai, W. (1977), "A simple and efficient finite element for plate bending", Int. J. Numer. Meth. Eng., 11, 1529-1542. https://doi.org/10.1002/nme.1620111005
  6. Kanok-Nukulchai, W., Dayawansa, P.H. and Karasudhi, P. (1981), "An exact finite element model for deep beams", International Journal of Structures, 1, 1-7.
  7. Krysl, P. and Belytschko, T. (1995), "Analysis of thin plates by the element-free Galerkin method", Comput. Mech., 17, 26-35. https://doi.org/10.1007/BF00356476
  8. Krysl, P. and Belytschko, T. (1996), "Analysis of thin shells by the element-free Galerkin method", Comput. Mech., 33, 3057-3080.
  9. Lancaster, P. and Salkauskas, K. (1981), "Surfaces generated by moving least squares methods", Math. Comp, 37, 141-158. https://doi.org/10.1090/S0025-5718-1981-0616367-1
  10. Ma, H.T. and Kanok-Nukulchai, W. (1989), "On the application of assumed strain methods," Proceedings of EASEC 2, Chiang Mai, Thailand, 11-13.
  11. Noguchi, H. (1997), "Application of element free Galerkin method to analysis of Mindlin type plate/shell problems", Proceedings of ICES 97, San Jose, Costa Rica, 918-923.
  12. Noguchi, H., Kawashima, T. and Miyamura, T. (2000), "Element free analyses of shell and spatial structures", Int. J. Numer. Meth. Eng., 47, 1215-1240. https://doi.org/10.1002/(SICI)1097-0207(20000228)47:6<1215::AID-NME834>3.0.CO;2-M
  13. Prathap, G. (1993), Finite Element Method in Structural Mechanics, Kluwer Academic Publishers, The Netherlands.
  14. Reddy, J.N., Wang, C.M. and Lam, K.Y. (1997), "Unified finite elements based on the classical and shear deformation theories of beams and axisymmetric circular plates", Communications in Numerical Methods in Engineering, 13, 495-510. https://doi.org/10.1002/(SICI)1099-0887(199706)13:6<495::AID-CNM82>3.0.CO;2-9

Cited by

  1. A coupled numerical approach for nonlinear dynamic fluid‐structure interaction analysis of a near‐bed submarine pipeline vol.25, pp.6, 2008, https://doi.org/10.1108/02644400810891553
  2. GEOMETRICALLY NONLINEAR ANALYSIS OF MICROSWITCHES USING THE LOCAL MESHFREE METHOD vol.05, pp.04, 2008, https://doi.org/10.1142/S0219876208001601
  3. Assessment of higher order transverse shear deformation theories for modeling and buckling analysis of FGM plates using RBF based meshless approach pp.1573-6105, 2018, https://doi.org/10.1108/MMMS-07-2017-0069
  4. Micromechanical failure analysis of composite materials subjected to biaxial and off-axis loading vol.62, pp.1, 2017, https://doi.org/10.12989/sem.2017.62.1.043