Investigation of the Accuracy of the Numerical Manifold Method on n-Sided Regular Elements for Crack Problems


Article Preview

The numerical manifold method (NMM) is a representative among different numerical methods for crack problems. Due to the independence of physical domain and the mathematical cover system, totally regular mathematical elements can be used in the NMM. In the present paper, the NMM is applied to solve 2-D linear elastic crack problems, together with the comparison study on the accuracy of n-sided regular mathematical elements, i.e., the triangular elements (n=3), the quadrilateral elements (n=4) and the hexagonal elements (n=6). Our numerical results show that among different elements, the regular hexagonal element is the best and the quadrilateral element is better than the triangular one.



Edited by:

Jing Guo




H. H. Zhang and J. X. Yan, "Investigation of the Accuracy of the Numerical Manifold Method on n-Sided Regular Elements for Crack Problems", Applied Mechanics and Materials, Vols. 157-158, pp. 1093-1096, 2012

Online since:

February 2012




[1] G.H. Shi, Manifold method of material analysis, in: Transaction of 9th Army Conference on Applied Mathematics and Computing, Minneapolis, Minnesota (1991) 57-76.

[2] R.J. Tsay, Y.J. Chiou, W.L. Chuang, Crack growth prediction by manifold method, J. Eng. Mech-ASCE, 125 (1999) 884-890.

[3] G.W. Ma, X.M. An, H.H. Zhang, et al, Modeling complex crack problems using the numerical manifold method, Int. J. Fracture, 156 (2009) 21-35.

[4] H.H. Zhang, L.X. Li, X.M. An, et al, Numerical analysis of 2-D crack propagation problems using the numerical manifold method, Eng. Anal. Bound. Elem. 34 (2010) 41-50.

[5] M. Kurumatani, K Terada, Finite cover method with multi-cover layers for the analysis of evolving discontinuities in heterogeneous media, Int. J. Numer. Meth. Eng. 79 (2009) 1-24.


[6] H.H. Zhang, S.Q. Zhang, Extract of stress intensity factors on honeycomb elements by the numerical manifold method, submitted to Finite Elem. Anal. Des. (2011).

[7] E.L. Wachspress, A rational finite element basis, Academic Press, New York, (1975).