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Computation of Stress Intensity Factors Using Wavelet-Based Element

  • J.-W. Xiang (a1) (a2), M. Liang (a2) and Y.-T. Zhong (a1)

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.

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1.Tada, H., Paris, P. C. and Irwin, G. R., The Stress Analysis of Cracks Handbook, 3rd Edition, ASME Press, New York, pp. 127142 (2000).
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. 837840 (1988).
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. 3235 (1985).
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. 2144 (1995).
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. 599610 (1993).
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. 309317(2013).
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. 318326 (2013).
8.Chao, C. K. and Wikarta, A., “Anti-Plane Interaction Between a Crack and an Elliptically Cylindrical Layered Media,” Journal of Mechanics, 29, pp. 8593 (2013).
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. 643651 (2013).
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. 347368 (2009).
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. 113125 (1996).
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. 99108 (2009).
13.Yang, X. Q., “A Special Crack Tip Displacement Discontinuity Element,” Mechanics Research Communication, 31, pp. 651659 (2004).
14.Meshii, T. and Watanabe, K., “Stress Intensity Factor Error Index for Finite Element Analysis with Singular Elements,” Engineering Fracture Mechanics, 70, pp. 657669 (2003).
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. 2242 (2014).
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. 297302 (2004).
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. 157169 (2005).
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. 123165 (2000).
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. 12691280 (2006).
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. 243255 (2008).
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. 416427(2010).
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. 15321540 (2014).
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. 34493466 (2013).
24.Cohen, A., Numerical Analysis of Wavelet Method, Elsevier Press, Amsterdam, pp. 3235 (2003).
25.Li, B. and Chen, X. F., “Wavelet-Based Numerical Analysis: A Review and Classification,” Finite Ele ments in Analysis and Design, 81, pp. 1431 (2014).
26.Chui, C. K. and Quak, E., “Wavelets on a Bounded Interval,” Numerical Methods in Approximation Theory, 9, pp. 5377 (1992).
27.Mallat, S., A Wavelet Tour of Signal Processing, Academic Press, London, pp. 134 (1999).
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Journal of Mechanics
  • ISSN: 1727-7191
  • EISSN: 1811-8216
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