Analysis and Prediction of Crack Propagation in Plates by the Enriched Free Galerkin Method
International Journal of Mechanical Engineering and Applications
Volume 2, Issue 6, December 2014, Pages: 78-86
Received: Nov. 6, 2014;
Accepted: Nov. 21, 2014;
Published: Nov. 25, 2014
Views 3585 Downloads 446
Bui Manh Tuan, School of Mechanical Engineering, Southeast University, Nanjing city, Jiangsu Province, China; Faculty of Mechanical Engineering, Tuy Hoa Industrial College, Tuy Hoa City, Phu Yen Province, Vietnam
Chen Yun Fei, School of Mechanical Engineering, Southeast University, Nanjing city, Jiangsu Province, China
This paper presents a centre and edge crack analysis using meshless methods which is based on moving least squares (MLS) approximation. The unknown displacement function u(x) is approximated by moving least square approximation uh(x). These approximation are constructed by using a weight function which is based a monomial basis function and a set of non-constant coefficients. A subdivision that is similar to finite element method is used to provide a background mesh for numerical integration. An enriched EFG formulation with fracture problems is proposed to improve the solution accuracy for linear elastic fracture problem. The essential boundary conditions are enforced by Lagrange multipliers method. A code has been written in Matlab for the analysis of a crack tip. The obtained results of the developed EFG-code were compared to available experimental data and other numerical (exact methods and finite element method) methods.
Bui Manh Tuan,
Chen Yun Fei,
Analysis and Prediction of Crack Propagation in Plates by the Enriched Free Galerkin Method, International Journal of Mechanical Engineering and Applications.
Vol. 2, No. 6,
2014, pp. 78-86.
S.T. Raveendra, P.K. Banerjee, “Boundary element analysis of cracks in thermally stresses planar structures,” Int. J. Solids Struct, vol. 29, 1992, pp. 2301–2317.
L.N. Gifford, P.D. Hilton, Stress intensity factors by enriched finite elements, Eng. Fract. Mech, vol.10, 1978, pp. 485–496.
M. Duflot, “The extended finite element method in thermo-elastic fracture mechanics,” Int. J. Numer. Methods Eng, Vol.74 , 2008, pp. 827–847.
Belytschko T, Lu YY, Gu L, “Element-free Galerkin methods,” International Journal for Numerical Methods in Engineering , 1994, vol.37, pp. 229–256.
Fleming M, Chu YA, Moran B, Belytschko T, “Enriched element-free Galerkin methods for crack tip fields,” Int J Numer Methods Eng, 1997, vol.40, pp. 1483–504.
Belytschko T, Gu L, Lu YY, “Fracture and crack growth by element-free Galerkin methods,” Modelling and Simulation in Materials Science and Engineering, 1994, vol. l2, pp. 519–534.
Belytschko T, Lu YY, Gu L, Tabbara M, “Element-free Galerkin methods for static and dynamic fracture,” International Journal of Solids and Structures 1995, vol.32, pp. 2547–2570.
Belytschko T, Tabbara M, “Dynamic fracture using element-free Galerkin methods,” International Journal for Numerical Methods in Engineering, 1996, vol.39, pp. 923–938.
Lancaster P, Salkauskas K, “Surfaces generated by moving least squares methods,” Math Comput, 1981, vol. 37, pp. 141–58.
Nguyen P, Rabczuk T, Bordas S, Duflot M, “Meshless methods: a review and Computer implementation aspects,” Math Comput Simul, 2008, vol.79, pp. 763–813.
Tada Hiroshi, Paris Paul, Irwin George, “The Stress Analysis of Cracks Handbook [M],” Washington University, 1957.
Dennis M Tracy, “Finite elements for determination of crack tip elastic stress intensity factors [J],” Engineering Fracture Mechanics, 1971, vol.3(3), pp. 255-266.
Moes N, Dolbow J, Belytschko T, “A finite element method for crack growth without remeshing,” International Journal for Numerical Methods in Engineering, 1999, vol.46(1), pp.131–150.
Ma wen tao, Li ning, Shi jun ping, “Modelling crack growth by enriched Meshless method based on partition of unity,” Chinese journal of computational Mechanics, 2013, vol.30, pp.28-33.
N. Muthu, S. K. Maiti, B. G. Falzon, I. Guiamatsia, “A comparison of stress intensity factors obtained through crack closure integral and other approaches using Xtended element-free Galerkin method,” Comput Mech, 2013, vol.52, pp. 587–605.
N. Muthu, B.G.Falzon, S.K.Maiti, S.Khoddam, “Modified crack closure integral technique for extraction of SIFs in mesh free methods,” Finite Elements in Analysis and Design, 2014, pp. 25–39.
Sayyed Shahram Ghorashi, Soheil Mohammadi, Saeed-Reza Sabbagh-Yazdi, “Orthotropic enriched element free Galerkin method for fracture analysis of composites”’ Engineering Fracture Mechanics, vol.78, 2012, pp. 1906–1927.
Kong, X.M., Schluter, N. Dahl, W, “Effect of triaxial stress on mixed-mode fracture,” Eng. Fract. Mech, 1995, vol.52(2), pp. 379–388.
Khan, Sh.M.A, Khraisheh. M.K, “A new criterion for mixed mode fracture initiation based on the crack tip plastic core region,” Int. J. Plast, 2004, vol.1, pp. 55–84.
Himanshu Pathak, Akhilendra Singh, Indra Vir Singh, “Fatigue crack growth simulations of homogeneous and bi-material interfacial cracks using element free Galerkin method,” Applied Mathematical Modelling, 2013, pp. 11-30.
Erdogan F, Sih GC, “On the crack extension in plates under plane loading and transverse shear,” J Basic Eng, 1963, vol.85, pp. 19–27.
I.V. Singh, B.K. Mishra, S. Bhattacharya, R.U. Patil, “The numerical simulation of fatigue crack growth using extended finite element method,” Int. J. Fatigue, 2011, vol.36, pp. 109–119.
BuiManhTuan, Chenyunfei, “Determine stress intensity factors and stress distribution for a surface crack in plates” Journal of Southeast University, 2014, vol.44 (4), pp. 728-734.
Marc Duflot, Hung Nguyen-Dang, “A meshless method with enriched weight functions for fatigue crack growth,” Int. J. Numer. Meth. Engng, 2004, vol.59, pp. 1945–1961.