Applications of numerical eigenfunctions in the fractal-like finite element method
Author(s)
Author(s)
Tsang, D. K. L.
Oyadiji, S. O.
Date Issued
2004
Publisher
John Wiley & Sons
Journal
International Journal for Numerical Methods in Engineering
Volume
61
Issue
4
Start page
475
End page
495
Abstract
The fractal-like finite element method is an accurate and efficient method to determine the stress intensity factors (SIF) around crack tips. The use of a self-similar mesh together with the William's eigenfunctions reduce the number of unknowns significantly. The SIFs are the primary unknowns and no post-processing is required. In all previous studies, we used the analytic eigenfunction expression to perform the global transformation. However, the eigenfunction cannot be found analytically in general crack problems. Two-dimensional axisymmetrical cracks are considered here. The resulting static equilibrium equations in local co-ordinates are non-homogeneous ordinary differential equations, for which the analytic eigenfunction cannot be found completely. We use a finite difference method to determine all the eigenfunctions needed numerically. Our evaluated SIF values show very close agreement with published results.
SFU Affiliated Publication
No
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