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Computation of Stress Intensity Factors Using Wavelet-Based Element

Published online by Cambridge University Press:  21 March 2016

J.-W. Xiang ,
M. Liang  and
Y.-T. Zhong
J.-W. Xiang*
Affiliation:
College of Mechanical & Electrical EngineeringWenzhou UniversityWenzhou, China Department of Mechanical EngineeringUniversity of OttawaOttawa, Canada
M. Liang
Affiliation:
Department of Mechanical EngineeringUniversity of OttawaOttawa, Canada
Y.-T. Zhong
Affiliation:
College of Mechanical & Electrical EngineeringWenzhou UniversityWenzhou, China
*
*Corresponding author ([email protected])
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Abstract

A new approach for the analysis of stress intensity factors (SIFs) for cracked plane plate is proposed based on the wavelet finite element method using the scaling functions of B-spline wavelet on the interval (BSWI). The performance of the method is investigated through the comparison of the results with the available numerical examples in the literate. It is shown that the solution quality is much better than that of the traditional adaptive finite element method. Though the method is applied to plane structures in this paper, it can be extended to solving problems for other classes of structures.

Keywords

PlateStress intensity factorsB-spline waveletWavelet-based element
Type
Research Article
Information
Journal of Mechanics , Volume 32 , Issue 3 , June 2016 , pp. N1 - N6
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2016 

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References

1.Tada, H., Paris, P. C. and Irwin, G. R., The Stress Analysis of Cracks Handbook, 3rd Edition, ASME Press, New York, pp. 127–142 (2000).Google Scholar
2.Huang, M. F. and Long, Y. Q., “Calculation of Stress Intensity Factors of Cracked Reissner Plates by the Sub-Region Mixed Finite Element Method,” Computers and Structures, 30, pp. 837–840 (1988).Google Scholar
3.Long, Y. and Zhao, Y., “Calculation of Stress Intensity Factors in Plane Problems by the Sub-Region Mixed Finite Element Method,” Advances in Engineering Software, 7, pp. 32–35 (1985).Google Scholar
4.Chen, W. H. and Yang, S. H., “Estimation of Stress Intensity Factors in Partially Patched Cracked Composite Laminates by Multilayer Hybrid-Stress Finite Element Method,” Finite Elements in Analysis and Design, 21, pp. 21–44 (1995).Google Scholar
5.Miyazaki, N., Ikeda, T., Soda, T. and Munakata, T., “Stress Intensity Factor Analysis of Interface Crack Using Boundary Element Method-Application of Contour-Integral Method,” Engineering Fracture Mechanics, 45, pp. 599–610 (1993).CrossRefGoogle Scholar
6.Lu, N. C., Cheng, Y. H. and Li, X. G., “Dynamic Problem Concerning Mode I Semi-Infinite Crack Propagation,” Journal of Mechanics, 29, pp. 309–317(2013).Google Scholar
7.Lu, N. C., Li, X. G. and Cheng, Y. H., “Asymmetrical Dynamic Propagation Problem on the Edges of Mode III Interface Crack Subjected to Superimpose Loads,” Journal of Mechanics, 29, pp. 318–326 (2013).Google Scholar
8.Chao, C. K. and Wikarta, A., “Anti-Plane Interaction Between a Crack and an Elliptically Cylindrical Layered Media,” Journal of Mechanics, 29, pp. 85–93 (2013).Google Scholar
9.Chao, C. K. and Lu, L. M., “Mode-III Stress Intensity Factors of an Arbitrarily Oriented Crack Crossing Interface in a Layered Structure,” Journal of Mechanics, 29, pp. 643–651 (2013).Google Scholar
10.Giner, E., Sukumar, N., Tarancón, J. E. and Fuenmayor, F. J., “An Abaqus Implementation of the Extended Finite Element Method,” Engineering Fracture Mechanics, 76, pp. 347–368 (2009).CrossRefGoogle Scholar
11.Kpegba, K. W. and Ottavy, N., “Stress Intensity Factors in Two-Dimensional Crack Problems by Using the Superimposed Meshes Method,” Engineering Fracture Mechanics, 54, pp. 113–125 (1996).Google Scholar
12.Souiyah, M., Alshoaibi, A., Muchtar, A. and Ariffin, A. K., “Two-Dimensional Finite Element Method for Stress Intensity Factor Using Adaptive Mesh Strategy,” Acta Mechanics, 204, pp. 99–108 (2009).Google Scholar
13.Yang, X. Q., “A Special Crack Tip Displacement Discontinuity Element,” Mechanics Research Communication, 31, pp. 651–659 (2004).Google Scholar
14.Meshii, T. and Watanabe, K., “Stress Intensity Factor Error Index for Finite Element Analysis with Singular Elements,” Engineering Fracture Mechanics, 70, pp. 657–669 (2003).CrossRefGoogle Scholar
15.Daimon, R. and Okada, H., “Mixed-Mode Stress Intensity Factor Evaluation by Interaction Integral Method for Quadratic Tetrahedral Finite Element with Correction Terms,” Engineering Fracture Mechanics, 115, pp. 22–42 (2014).Google Scholar
16.Chiang, C. H. and Cheng, C. C., “Detecting Rebars and Tubes Inside Concrete Slabs Using Continuous Wavelet Transform of Elastic Waves,” Journal of Mechanics, 20, pp. 297–302 (2004).Google Scholar
17.Yang, T. S., Shy, S. S. and Chyou, Y. P., “Spatiotemporal Intermittency Measurements in a Gas-Phase Near-Isotropic Turbulence Using High-Speed DPIV and Wavelet Analysis,” Journal of Mechanics, 21, pp. 157–169 (2005).Google Scholar
18.Canute, C., Tabacco, A. and Urban, K., “The Wavelet Element Method Part II: Realization and Additional Feature in 2D and 3D,” Applied and Computational Harmonic Analysis, 8, pp. 123–165 (2000).Google Scholar
19.Xiang, J. W., Chen, X. F., He, Y. M. and He, Z. J., “The Construction of Plane Elastomechanics and Mindlin Plate Elements of B-Spline Wavelet on the Interval,” Finite Elements in Analysis and Design, 42, pp. 1269–1280 (2006).Google Scholar
20.Xiang, J. W., Chen, X. F., He, Z. J. and Zhang, Y. H., “A New Wavelet-Based Thin Plate Element Using B-Spline Wavelet on the Interval,” Computational Mechanics, 41, pp. 243–255 (2008).Google Scholar
21.Zhang, X. W., Chen, X. F. and Wang, X. Z., “Multivariable Finite Elements Based on B-Spline Wavelet on the Interval for Thin Plate Static and Vibration Analysis,” Finite Elements in Analysis and Design, 46, pp. 416–427(2010).Google Scholar
22.Zhang, X. W., Chen, X. F. and Yang, Z. B., “Multivariable Wavelet Finite Element for Flexible Skew Thin Plate Analysis,” Science in China Technology Science, 57, pp. 1532–1540 (2014).Google Scholar
23.Yang, Z. B., Chen, X. F. and Zhang, X. W., “Free Vibration and Buckling Analysis of Plates Using B-Spline Wavelet on the Interval Mindlin Element,“ Applied Mathematical Modeling, 37, pp. 3449–3466 (2013).Google Scholar
24.Cohen, A., Numerical Analysis of Wavelet Method, Elsevier Press, Amsterdam, pp. 32–35 (2003).Google Scholar
25.Li, B. and Chen, X. F., “Wavelet-Based Numerical Analysis: A Review and Classification,” Finite Ele ments in Analysis and Design, 81, pp. 14–31 (2014).Google Scholar
26.Chui, C. K. and Quak, E., “Wavelets on a Bounded Interval,” Numerical Methods in Approximation Theory, 9, pp. 53–77 (1992).Google Scholar
27.Mallat, S., A Wavelet Tour of Signal Processing, Academic Press, London, pp. 1–34 (1999).Google Scholar