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Analysis of Cracked Plates Using Localized Multi-Domain Differential Quadrature Method
Applied and Computational Mathematics
Volume 2, Issue 4, August 2013, Pages: 109-114
Received: Aug. 5, 2013; Published: Aug. 30, 2013
Authors
Tharwat Osman, Dept. of Math. And Phys., Faculty of Engineering, Zagazig University, Zagazig, Egypt
Mohamed. S. Matbuly, Dept. of Math. And Phys., Faculty of Engineering, Zagazig University, Zagazig, Egypt
Salwa. A. Mohamed, Dept. of Math. And Phys., Faculty of Engineering, Zagazig University, Zagazig, Egypt
Mohamed Nassar, Dept. of Math. And Phys., Faculty of Engineering, Cairo University, Giza, Egypt
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Abstract
In this paper, A multi-domain differential quadrature method is employed to solve a mode III crack problem. The domain of the problem is assumed to be irregular rather than it possesses discontinuities, (cracks). The entire domain is divided into several subdomains, according to the crack locations. A conformal mapping is applied to transform the irregular subdomains to regular ones. Then the differential quadrature method is employed to solve the problem over the transformed domains. Further, it’s focused on the crack regions by applying the localized version of differential quadrature method. The out of plane deflection is obtained at the immediate vicinity of the crack tips, such that the stress intensity factor can be calculated. The obtained results are compared with the previous analytical ones. Furthermore a parametric study is introduced to investigate the effects of elastic and geometric characteristics on the values of stress intensity factor.
Keywords
Irregular, Localized Differential Quadrature, Conformal Mapping, Mode III, Stress Intensity Factor
Tharwat Osman, Mohamed. S. Matbuly, Salwa. A. Mohamed, Mohamed Nassar, Analysis of Cracked Plates Using Localized Multi-Domain Differential Quadrature Method, Applied and Computational Mathematics. Vol. 2, No. 4, 2013, pp. 109-114. doi: 10.11648/j.acm.20130204.12
References
[1]
Bora Yildirim, Özge Kutlu and Suat Kadioğlu, "Periodic crack problem for a functionally graded half-plane an analytic solution", International Journal of Solids and Structures, Vol. 48, pp. 3020–3031, 2011.
[2]
H. G. Beom, J. W. Lee and C. B. Cui, " Analysis of a kinked crack in an anisotropic material under antiplane deformation", Journal of Mechanical Science and Technology, Vol. 26, pp. 411–419, 2012.
[3]
Jeong Woo Shin and Young-Shin Lee, "Anti-plane moving crack in a functionally graded piezoelectric layer between two dissimilar piezoelectric strips", Journal of Mechanical Science and Technology, Vol. 26, pp. 1017–1025, 2012.
[4]
E. Wyart, D. Coulon, T. pardoen, J.F. Remacle and F. Lani, "Application of the sub- structured finite element/extended finite element method (S-FE/XFE) to the analysis of cracks in aircraft thin walled structures", Engineering Fracture Mechanics, Vol. 76, pp. 44–58, 2009.
[5]
Jin-Shi Wen, Woo-Eon Ju, Tae-Kyung Han, Seung Tae Choi1 and Kyung-Sick Lee, "Finite element analysis of a subsurface penny-shaped crack with crack-face contact and friction under a moving compressive load", Journal of Mechanical Science and Technology, Vol. 26, pp. 2719-2726, 2012.
[6]
Jingbo Duan, Yongjun Lei and Daokui Li, "Enriched finite element method for 2-D and 3-D blunt crack problems in a viscoelastic medium", Journal of Mechanical Science and Technology, Vol. 26, pp. 869-882, 2012.
[7]
Jun Lei, Felipe Garcia-Sanchez, Michael Wunsche, Chüanzeng, Yue-Sheng Wang and Andres Saez, " Dynamic analysis of interfacial crack problems in anisotropic bi-materials by a time-domain BEM", Engineering Fracture Mechanics, Vol. 76, pp. 1996–2010, 2009.
[8]
X. Yan, B. Liu and J. Yu, "Cracks emanating from a square hole in rectangular plate in tension", Fatigue Fract Engng Mater Struct, Vol. 35, pp. 238–246, 2011.
[9]
X. Yan and B. Liu, "Rectangular Tensile Sheet with Double Edge Notch Cracks", Fatigue Fract Engng Mater Struct, Vol. 35, pp. 466–475, 2012.
[10]
Zhangxian Yuan and Xinwei Wang, "Buckling and post-buckling analysis of extensible beam–columns by using the differential quadrature method", Computers and Mathematics with Applications, Vol. 62, pp. 4499–4513, 2011.
[11]
S. Hamed Meraji, Abbas Ghaheri and Parviz Malekzadeh, "An efficient algorithm based on the differential quadrature method for solving Navier–Stokes equations", International Journal for Numerical Methods in Fluids, (2012), Published online in Wiley Online Library (wileyonlinelibrary.com).
[12]
Mohamed Nassar, Mohamed S. Matbuly and Ola Ragb,"Vibration analysis of structural elements using differential quadrature method", Journal of Advanced Research, Vol. 4, pp. 93–102, 2013.
[13]
M. Mallakzadeh, A. A. Pasha Zanoosi and A. Alibeigloo , "Fundamental frequency analysis of microtubules under different boundary conditions using differential quadrature method", Communications in Nonlinear Science and Numerical Simulation, Vol. 18, No. 8, pp. 2240–2251, 2013.
[14]
F. L. Liu and K.M. Liew, "Differential quadrature element method: a new approach for free vibration analysis of polar Mindlin plates having discontinuities", Comput. Methods Appl. Mech. Engrg., Vol. 179, pp. 407-423, 1999.
[15]
F.-L. Liu, "Differential quadrature element method for buckling analysis of rectangular Mindlin plates having discontinuities", International Journal of Solids and Structures, Vol. 38, pp. 2305-2321, 2001.
[16]
Hongzhi Zhong and Yuhong ,"A note on incorporation of domain decomposition into the differential quadrature method", Communications in Numerical Methods in Engineering Commun. Numer. Meth. Engng., Vol. 19, pp. 297–306, 2003.
[17]
Xionghua Wu and YE Shen," Differential Quadrature Domain Decomposition Method for A Class Of Parabolic Equations", Computers And Mathematics With Applications, Vol. 48, pp. 1819-1832, 2004.
[18]
Z. Zong, K. Y. Lam and Y. Y. Zhang, "A Multidomain Differential Quadrature Approach To Plane Elastic Problems With Material Discontinuty", Mathematical and Computer Modelling, Vol. 41, pp. 539-553, 2005.
[19]
C. Shu,W. X. Wu, H. Ding and C. M. Wang, "Free Vibration Analysis of Curvilinear Quadrilateral Plates by the Differential Quadrature Method", Journal of Computational Physics, Vol. 163, pp. 452–466, 2000.
[20]
Chang Shu,"Differential Quadrature and Its Application in Engineering", London springer, Verlag, 2000
[21]
Liangliang Du and Xionghua Wu;" On a rational differential quadrature method in irregular domains for problems with boundary layers", Applied Mathematics and Computation, Vol. 218, pp. 1379–1388, 2011.
[22]
C.H. Tsai, D. I. Young and C. C. Hsiang," The localized differential quadrature method for two-dimensional stream function formulation of Navier–Stokes equations ", Engineering Analysis with Boundary Elements, Vol. 35, pp. 1190–1203, 2011.
[23]
M.E. Hamidi, M. R. Hashemi, N. Talebbeydokhti and S. P. Neill," numerical modeling of the mild slope equation using localized differential quadrature method", Ocean Engineering, Vol. 47, pp. 88–103, 2012.
[24]
David J. Unger "Analytical fracture mechanics" Academic press, London, 1995.
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