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Computation of Plane Crack Stress Intensity Factors Using Trigonometric Wavelet Finite Element Method
Author(s) -
HE W.Y.,
REN W.X.,
YANG Z.J.
Publication year - 2012
Publication title -
fatigue and fracture of engineering materials and structures
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.887
H-Index - 84
eISSN - 1460-2695
pISSN - 8756-758X
DOI - 10.1111/j.1460-2695.2011.01626.x
Subject(s) - wavelet , finite element method , extrapolation , mathematics , cascade algorithm , trigonometric functions , mathematical analysis , interpolation (computer graphics) , stress intensity factor , extended finite element method , algorithm , wavelet packet decomposition , wavelet transform , geometry , structural engineering , computer science , artificial intelligence , engineering , motion (physics)
The trigonometric wavelet has both good approximation characteristics of trigonometric function and multi‐resolution, local characteristics of wavelet. It is used in this study as interpolation functions in the finite element (FE) method. FE formulations for elastic plane problems are derived based on the principle of minimum potential energy. Stress intensity factors of plane stress problems with cracks are computed based on the displacement extrapolation technique. The wavelet hierarchical and multi‐resolution approaches are also used to improve accuracy of calculations. Numerical examples have shown that the proposed trigonometric wavelet finite element formulations are effective for computing the stress intensity factors with a small number of elements. Both wavelet hierarchical and wavelet multi‐resolution methods lead to improved computational accuracy. They can be selected according to the problems to be solved.