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How to cite this paper
APA: Ham, S & Hong, H. (2018). XFEM fracture analysis by applying smoothed weighted functions with compact support. Engineering Solid Mechanics, 6(3), 227-240.
Chicago/Turabian: Ham, S & Hong, H. 2018. "XFEM fracture analysis by applying smoothed weighted functions with compact support." Engineering Solid Mechanics 6, no. 3 (2018): 227-240.
AMA: Ham, S & Hong, H. XFEM fracture analysis by applying smoothed weighted functions with compact support. Engineering Solid Mechanics. 2018;6(3):227-240.
References
Amiri, F., Anitescu, C., Arroyo, M., Bordas, S. P. A., & Rabczuk, T. (2014). XLME interpolants, a seamless bridge between XFEM and enriched meshless methods. Computational Mechanics, 53(1), 45-57.
Areias, P., Msekh, M. A, & Rabczuk, T. (2016). Damage and fracture algorithm using the screened Poisson equation and local remeshing. Engineering Fracture Mechanics, 158, 116-143.
Areias, P., Reinoso, J., & Camanho, P. P (2015). A constitutive-based element by- element crack propagation algorithm with local mesh refinement. Computational Mechanics, 56(2), 291-315
Areias, P., Rabczuk, T., & Dias-da-Costa, D. (2013). Element-wise fracture algorithm based on rotation of edges. Engineering Fracture Mechanics, 110, 113-137
Areias, P., & Rabczuk, T. (2013). Finite strain fracture of plates and shells with configurational forces and edge rotation. International Journal for Numerical Methods in Engineering, 94(12), 1099-1122.
Areias, P., Dias-da-Costa, D., Alfaiate, J., & Julio, E. (2009). Arbitrary bi-dimensional finite strain cohesive crack propagation. Computational Mechanics, 45(1), 1741-1760.
Belytschko, T., & Black, T. (1999). Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering, 45(5), 601-620.
Bittencourt, T. N., Ingraffea, A. R., Wawrzynek, P. A., & Sousa, J. L. (1996). Quasi-automatic simulation of crack propagation for 2D LEFM problems. Engineering Fracture Mechanics, 55(2), 321-334.
Bourdin, B., Francfort, G. A., & Marigo, J. -J. (2000). Numerical experiments in revisited brittle fracture. Journal of Mechanics and Physics of Solids, 48, 797-826.
Chahine, E., Laborde, P. & Renard, Y. (2008). Crack tip enrichment in the XFEM using a cutoff function. International Journal for Numerical Methods in Engineering, 75, 629-646.
Chessa, J., Wang, H., Belytschko, T. (2003). On the construction of blending elements for local partition of unity enriched finite elements. International Journal for Numerical Methods in Engineering, 57, 1015-1038.
Erdogan, F., (2000). Fracture mechanics. International journal of solids and structures, 37, 171-183.
Franke, C., & Schaback, R. (1997). Solving Partial Differential Equations by Collocation Using Radial Basis Functions. Applied Mathematics and Computation, 93, 73-82.
Fries, T. P., (2008). A corrected XFEM approximation without problems in blending elements. International Journal for Numerical Methods in Engineering, 75, 503-532.
Goangseup, Z., Timon, R., & Wolfgang, W. (2007). Extended Meshfree Methods without Branch Enrichment for Cohesive Cracks. Computational Mechanics, 40(2), 367-382.
Gracie, R., Wang, H., & Belytschko, T. (2008). Blending in the extended finite element method by discontinuous Galerkin and assumed strain methods. International Journal for Numerical Methods in Engineering, 74, 1645-1669.
Hansbo, A,, & Hansbo, P. (2004). A finite element method for the simulation of strong and weak discontinuities in solid mechanics. Computer Methods in Applied Mechanics and Engineering, 193, 3523-3540.
Kansa, E. J. (1990). Multiquadrics-A Scattered Data Approximation Scheme with Applications to Computational Fluid dynamics. Computers and Mathematical Application, 19(8/9), 127-145.
Karihalloo, B. L., & Xiao, Q. Z. (2003). Modeling of stationary and growing cracks in FE framework without remeshing: a state-of-the-art review. Computational Structure, 81, 119-129.
Liu, G. R., & Gu, Y. T. (2005). An introduction to meshfree methods and their programming. Netherlands: Springer.
Loehnert, S., & Belytschko, T. (2007). A multiscale projection method for macro/microcrack simulations. International Journal for Numerical Methods in Engineering, 71, 1466-1482.
Melenk, J. M, & Babuska, I. (1996). The partition of unity finite element method: Basic theory and applications. Computer Methods in Applied Mechanics and Engineering, 139, 289-314.
Miehe, C., & Gurses, E. (2007). A robust algorithm for configurational-force-driven brittle crack propagation with r-adaptive mesh alignment. International Journal for Numerical Methods in Engineering, 72, 127-155.
Moёs, N., Dolbow, J., & Belytschko, T. (1999). A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering, 46(1), 131-150.
Moёs, N., Dolbow, J., & Belytschko, T. (1999). A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering, 46, 131-150.
Oliver. J., (1989). A consistent characteristic length for smeared cracking models. International Journal for Numerical Methods in Engineering, 28, 461-474.
Rabczuk, T., & Belytschko, T. (2004). Cracking particles: a simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering, 61(13), 2316-2343.
Rabczuk, T., & Zi, G. (2007). A meshfree method based on the local partition of unity for cohesive cracks. Computational Mechanics, 39(6), 743-760.
Sharan, M., Kansa, E. J., & Gupta, S. (1997). Application of the Multiquadric Method for Numerical Solution of Elliptic Partial Differential Equations. Applied Mathematics and Computation, 84, 275-302.
Shibanuma, K., Utsunomiya, T. (2008). PUFEM-based XFEM for avoiding the problem of blending elements. The 21st KKCNN Symposium on Civil Engineering, Singapore.
Sukumar, N., Chopp, D. L., Moes, N., & Belytschko, T. (2001). Modeling holes and inclusions by level sets in the extended finite-element method. Computer Methods in Applied Mechanics and Engineering, 190, 6183-6200.
Tarancon, J. E., Vercher, A., Giner, E., & Fuenmayor, F. J. (2009). Enhanced blending elements for XFEM applied to linear elastic fracture mechanics. International Journal for Numerical Methods in Engineering, 77, 126-148.
Timon, R., Stephane, B., & Goangseup, Z. (2010). On three-dimensional modelling of crack growth using partition of unity methods. Computers & Structures, 88(23-24), 1391-1411.
Ventura, G., Gracie, R., & Belytschko, T. (2009). Fast integration and weight function blending in the extended finite element method. International Journal for Numerical Methods in Engineering, 77, 1-29.
Ventura, G., Xu, J. X., & Belytschko, T. (2002). Vector level set method and new discontinuity approximations for crack growth by EFG. International Journal of Numerical Methods in Engineering, 54(6), 923-944.
Wu, Z. (1995). Compactly supported positive definite radial functions. Advances in Computational Mathematics, 4, 283-292.
Wendland, H. (1998). Error estimates for interpolation by compactly supported radial basis functions of minimal degree. Journal of Approximation Theory, 93, 258-396.
Wendland, H. (1995). Piecewise polynomial, positive definite and compactly supported radial basis functions of minimal degree. Advances in Computational Mathematics, 4, 389-396.
Areias, P., Msekh, M. A, & Rabczuk, T. (2016). Damage and fracture algorithm using the screened Poisson equation and local remeshing. Engineering Fracture Mechanics, 158, 116-143.
Areias, P., Reinoso, J., & Camanho, P. P (2015). A constitutive-based element by- element crack propagation algorithm with local mesh refinement. Computational Mechanics, 56(2), 291-315
Areias, P., Rabczuk, T., & Dias-da-Costa, D. (2013). Element-wise fracture algorithm based on rotation of edges. Engineering Fracture Mechanics, 110, 113-137
Areias, P., & Rabczuk, T. (2013). Finite strain fracture of plates and shells with configurational forces and edge rotation. International Journal for Numerical Methods in Engineering, 94(12), 1099-1122.
Areias, P., Dias-da-Costa, D., Alfaiate, J., & Julio, E. (2009). Arbitrary bi-dimensional finite strain cohesive crack propagation. Computational Mechanics, 45(1), 1741-1760.
Belytschko, T., & Black, T. (1999). Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering, 45(5), 601-620.
Bittencourt, T. N., Ingraffea, A. R., Wawrzynek, P. A., & Sousa, J. L. (1996). Quasi-automatic simulation of crack propagation for 2D LEFM problems. Engineering Fracture Mechanics, 55(2), 321-334.
Bourdin, B., Francfort, G. A., & Marigo, J. -J. (2000). Numerical experiments in revisited brittle fracture. Journal of Mechanics and Physics of Solids, 48, 797-826.
Chahine, E., Laborde, P. & Renard, Y. (2008). Crack tip enrichment in the XFEM using a cutoff function. International Journal for Numerical Methods in Engineering, 75, 629-646.
Chessa, J., Wang, H., Belytschko, T. (2003). On the construction of blending elements for local partition of unity enriched finite elements. International Journal for Numerical Methods in Engineering, 57, 1015-1038.
Erdogan, F., (2000). Fracture mechanics. International journal of solids and structures, 37, 171-183.
Franke, C., & Schaback, R. (1997). Solving Partial Differential Equations by Collocation Using Radial Basis Functions. Applied Mathematics and Computation, 93, 73-82.
Fries, T. P., (2008). A corrected XFEM approximation without problems in blending elements. International Journal for Numerical Methods in Engineering, 75, 503-532.
Goangseup, Z., Timon, R., & Wolfgang, W. (2007). Extended Meshfree Methods without Branch Enrichment for Cohesive Cracks. Computational Mechanics, 40(2), 367-382.
Gracie, R., Wang, H., & Belytschko, T. (2008). Blending in the extended finite element method by discontinuous Galerkin and assumed strain methods. International Journal for Numerical Methods in Engineering, 74, 1645-1669.
Hansbo, A,, & Hansbo, P. (2004). A finite element method for the simulation of strong and weak discontinuities in solid mechanics. Computer Methods in Applied Mechanics and Engineering, 193, 3523-3540.
Kansa, E. J. (1990). Multiquadrics-A Scattered Data Approximation Scheme with Applications to Computational Fluid dynamics. Computers and Mathematical Application, 19(8/9), 127-145.
Karihalloo, B. L., & Xiao, Q. Z. (2003). Modeling of stationary and growing cracks in FE framework without remeshing: a state-of-the-art review. Computational Structure, 81, 119-129.
Liu, G. R., & Gu, Y. T. (2005). An introduction to meshfree methods and their programming. Netherlands: Springer.
Loehnert, S., & Belytschko, T. (2007). A multiscale projection method for macro/microcrack simulations. International Journal for Numerical Methods in Engineering, 71, 1466-1482.
Melenk, J. M, & Babuska, I. (1996). The partition of unity finite element method: Basic theory and applications. Computer Methods in Applied Mechanics and Engineering, 139, 289-314.
Miehe, C., & Gurses, E. (2007). A robust algorithm for configurational-force-driven brittle crack propagation with r-adaptive mesh alignment. International Journal for Numerical Methods in Engineering, 72, 127-155.
Moёs, N., Dolbow, J., & Belytschko, T. (1999). A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering, 46(1), 131-150.
Moёs, N., Dolbow, J., & Belytschko, T. (1999). A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering, 46, 131-150.
Oliver. J., (1989). A consistent characteristic length for smeared cracking models. International Journal for Numerical Methods in Engineering, 28, 461-474.
Rabczuk, T., & Belytschko, T. (2004). Cracking particles: a simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering, 61(13), 2316-2343.
Rabczuk, T., & Zi, G. (2007). A meshfree method based on the local partition of unity for cohesive cracks. Computational Mechanics, 39(6), 743-760.
Sharan, M., Kansa, E. J., & Gupta, S. (1997). Application of the Multiquadric Method for Numerical Solution of Elliptic Partial Differential Equations. Applied Mathematics and Computation, 84, 275-302.
Shibanuma, K., Utsunomiya, T. (2008). PUFEM-based XFEM for avoiding the problem of blending elements. The 21st KKCNN Symposium on Civil Engineering, Singapore.
Sukumar, N., Chopp, D. L., Moes, N., & Belytschko, T. (2001). Modeling holes and inclusions by level sets in the extended finite-element method. Computer Methods in Applied Mechanics and Engineering, 190, 6183-6200.
Tarancon, J. E., Vercher, A., Giner, E., & Fuenmayor, F. J. (2009). Enhanced blending elements for XFEM applied to linear elastic fracture mechanics. International Journal for Numerical Methods in Engineering, 77, 126-148.
Timon, R., Stephane, B., & Goangseup, Z. (2010). On three-dimensional modelling of crack growth using partition of unity methods. Computers & Structures, 88(23-24), 1391-1411.
Ventura, G., Gracie, R., & Belytschko, T. (2009). Fast integration and weight function blending in the extended finite element method. International Journal for Numerical Methods in Engineering, 77, 1-29.
Ventura, G., Xu, J. X., & Belytschko, T. (2002). Vector level set method and new discontinuity approximations for crack growth by EFG. International Journal of Numerical Methods in Engineering, 54(6), 923-944.
Wu, Z. (1995). Compactly supported positive definite radial functions. Advances in Computational Mathematics, 4, 283-292.
Wendland, H. (1998). Error estimates for interpolation by compactly supported radial basis functions of minimal degree. Journal of Approximation Theory, 93, 258-396.
Wendland, H. (1995). Piecewise polynomial, positive definite and compactly supported radial basis functions of minimal degree. Advances in Computational Mathematics, 4, 389-396.