Natural Element Method for Material and Geometrical Bi-Nonlinear Problems

Abstract:

Based on the Voronoi diagram of some nodes, the natural element method (NEM) constructs the shape functions by the natural neighbor interpolation method, and its shape functions satisfy the Kronecker delta property, which makes it impose essential boundary conditions easily. Based on the geometrical nonlinear relations and material nonlinear constitutive relations, we extend the NEM to material and geometrical bi-nonlinear problems in this paper. Numerical examples show that the NEM is effective, rational and feasible in dealing with problems of both material and geometrical bi-nonlinear.

• Periodical: Applied Mechanics and Materials (Volumes 166-169)
• Pages: 93-97
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.166-169.93
• Online since: May 2012
• Authors: Dao Hong Ding, Qing Zhang, Jiang Qing Xiao
• Keywords: Geometrical Nonlinear Problem, Material Nonlinear Problem, Natural Element Method, Natural Neighbor Interpolation, Numerical Method

References

[1] J. Braun, M.Sambridge: Nature, Vol.376 (1995), p.655

[2] E. Cueto, N. Sukumar, B. Calvo, et al.: Arch. Comput. Method. Eng., Vol.10 (2003), p.307

[3] N. Sukumar, B. Moran, T. Belytschko: Int. J. Numer. Meth. Engng. Vol.43 (1998), p.839

[4] N. Sukumar, B. Moran, A.Y. Semenov, et al: Int. J. Numer. Meth. Engng. Vol.50 (2001), p.1

[5] D. Bueche, N. Sukumar, B. Moran: Comput. Mech. Vol.25 (2000), p.207

[6] J. R. Cho, H. W. Lee: Comput. Struct. Vol.84 (2006), p.293

[7] D. H. Ding, Q. Zhang, L. Y. Luo, in: 2011 International Conference on Remote Sensing, Environment and Transportation Engineering (RSETE) (2011).

[8] J. T. Holden: Int.J.So lids Struc. Vol. 8 (1972), p.1051