How to cite this paper
Ton-That, H. (2020). Improvement on eight-node quadrilateral element (IQ8) using twice-interpolation strategy for linear elastic fracture mechanics.Engineering Solid Mechanics, 8(4), 323-336.
Refrences
Aliabadi, M. H., Cartwright, D. J., & Rooke, D. P. (1989). Fracture-mechanics weight-functions by the removal of singular fields using boundary element analysis. International Journal of Fracture, 40(4), 271-284.
Anderssohn, R., Hofmann, M., & Bahr, H. A. (2018). FEM-bifurcation analysis for 3D crack patterns. Engineering Fracture Mechanics, 202, 363-374.
Barsoum, R. S. (1974). Application of quadratic isoparametric finite elements in linear fracture mechanics. International Journal of Fracture, 10(4), 603-605.
Bathe, K.-J. (2006). Finite element procedures. USA: Prentice Hall, Pearson Education, Inc.
Bergara, A., Dorado, J. I., Martin-Meizoso, A., & Martínez-Esnaola, J. M. (2017). Fatigue crack propagation in complex stress fields: Experiments and numerical simulations using the Extended Finite Element Method (XFEM). International Journal of Fatigue, 103, 112-121.
Bhardwaj, G., Singh, I. V., & Mishra, B. K. (2013). Numerical Simulation of Plane Crack Problems Using Extended Isogeometric Analysis. Procedia Engineering, 64, 661-670.
Bui, T. Q. (2015a). Extended isogeometric dynamic and static fracture analysis for cracks in piezoelectric materials using NURBS. Computer Methods in Applied Mechanics and Engineering, 295(Supplement C), 470-509.
Bui, T. Q. (2015b). Extended isogeometric dynamic and static fracture analysis for cracks in piezoelectric materials using NURBS. Computer Methods in Applied Mechanics and Engineering, 295, 470-509.
Bui, T. Q., Do, T. V., Ton, L. H. T., Doan, D. H., Tanaka, S., Pham, D. T., . . . Hirose, S. (2016). On the high temperature mechanical behaviors analysis of heated functionally graded plates using FEM and a new third-order shear deformation plate theory. Composites Part B: Engineering, 92, 218-241.
Bui, T. Q., Vo, D. Q., Zhang, C., & Nguyen, D. D. (2014). A consecutive-interpolation quadrilateral element (CQ4): Formulation and applications. Finite Elements in Analysis and Design, 84, 14-31.
Chau-Dinh, T., Mai-Van, C., Zi, G., & Rabczuk, T. (2018). New kinematical constraints of cracked MITC4 shell elements based on the phantom-node method for fracture analysis. Engineering Fracture Mechanics, 199, 159-178.
Chau-Dinh, T., & Zi, G. (2011). A Phantom-Node Method for Predicting Residual Strength in Shell Structures with a Single Crack Based on a Crack Tip Opening Angle Criterion. Procedia Engineering, 14, 630-635.
Chau-Dinh, T., Zi, G., Lee, P.-S., Rabczuk, T., & Song, J.-H. (2012). Phantom-node method for shell models with arbitrary cracks. Computers & Structures, 92-93, 242-256.
Chen, H., Wang, Q., Liu, G. R., Wang, Y., & Sun, J. (2016). Simulation of thermoelastic crack problems using singular edge-based smoothed finite element method. International Journal of Mechanical Sciences, 115-116, 123-134.
Chen, L., Liu, G. R., Jiang, Y., Zeng, K., & Zhang, J. (2011). A singular edge-based smoothed finite element method (ES-FEM) for crack analyses in anisotropic media. Engineering Fracture Mechanics, 78(1), 85-109.
Denda, M., & Marante, M. E. (2004). Mixed mode BEM analysis of multiple curvilinear cracks in the general anisotropic solids by the crack tip singular element. International Journal of Solids and Structures, 41(5), 1473-1489.
Duan, J. B., Lei, Y. J., & Li, D. K. (2011). Fracture analysis of linear viscoelastic materials using triangular enriched crack tip elements. Finite Elements in Analysis and Design, 47(10), 1157-1168.
Ewalds, H., & Wanhill, R. (1989). Fracture Mechanics. New York: Edward Arnold.
Fawkes, A. J., Owen, D. R. J., & Luxmoore, A. R. (1979). An assessment of crack tip singularity models for use with isoparametric elements. Engineering Fracture Mechanics, 11(1), 143-159.
Feng, S. Z., & Li, W. (2018). An accurate and efficient algorithm for the simulation of fatigue crack growth based on XFEM and combined approximations. Applied Mathematical Modelling, 55, 600-615.
Gall, K., Sehitoglu, H., & Kadioglu, Y. (1996). FEM study of fatigue crack closure under double slip. Acta Materialia, 44(10), 3955-3965.
Giner, E., Sukumar, N., Tarancón, J. E., & Fuenmayor, F. J. (2009). An Abaqus implementation of the extended finite element method. Engineering Fracture Mechanics, 76(3), 347-368.
Henshell, R. D., & Shaw, K. G. (1975). Crack tip finite elements are unnecessary. International Journal for Numerical Methods in Engineering, 9(3), 495-507.
Hu, X., Bui, T. Q., Wang, J., Yao, W., Ton, L. H. T., Singh, I. V., & Tanaka, S. (2017). A new cohesive crack tip symplectic analytical singular element involving plastic zone length for fatigue crack growth prediction under variable amplitude cyclic loading. European Journal of Mechanics - A/Solids, 65, 79-90.
Jayaswal, K., & Grosse, I. R. (1993). Finite element error estimation for crack tip singular elements. Finite Elements in Analysis and Design, 14(1), 17-35.
Kang, Z., Bui, T. Q., Nguyen, D. D., Saitoh, T., & Hirose, S. (2015). An extended consecutive-interpolation quadrilateral element (XCQ4) applied to linear elastic fracture mechanics. Acta Mechanica, 226(12), 3991-4015.
Kumar, S., Singh, I. V., & Mishra, B. K. (2015). A homogenized XFEM approach to simulate fatigue crack growth problems. Computers & Structures, 150(Supplement C), 1-22.
Kuna, M. (2013). Finite Elements in Fracture Mechanics: Theory - Numerics - Applications: Springer Science & Business Media.
Kwon, Y. W., & Akin, J. E. (1989). Development of a derivative singular element for application to crack propagation problems. Computers & Structures, 31(3), 467-471.
Liu, P., Bui, T. Q., Zhang, C., Yu, T. T., Liu, G. R., & Golub, M. V. (2012). The singular edge-based smoothed finite element method for stationary dynamic crack problems in 2D elastic solids. Computer Methods in Applied Mechanics and Engineering, 233-236(Supplement C), 68-80.
Moës, 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.
Nash Gifford, L., & Hilton, P. D. (1978). Stress intensity factors by enriched finite elements. Engineering Fracture Mechanics, 10(3), 485-496.
Nguyen-Van, H., Ton-That, H. L., Chau-Dinh, T., & Dao, N. D. (2018). Nonlinear Static Bending Analysis of Functionally Graded Plates Using MISQ24 Elements with Drilling Rotations. Paper presented at the Proceedings of the International Conference on Advances in Computational Mechanics 2017, Singapore.
Nguyen-Xuan, H., Liu, G. R., Nourbakhshnia, N., & Chen, L. (2012). A novel singular ES-FEM for crack growth simulation. Engineering Fracture Mechanics, 84, 41-66.
Olgierd Cecil Zienkiewicz, Kenneth Morgan, & Morgan, K. (2006). Finite elements and approximation: Courier Corporation.
Olgierd Cecil Zienkiewicz, Robert L Taylor, Perumal Nithiarasu, & Zhu, J. (1977). The finite element method: McGraw-hill.
Oliva, V., Cséplö, L., Materna, A., & Bláhová, L. (1997). FEM simulation of fatigue crack growth. Materials Science and Engineering: A, 234-236, 517-520.
Oliveira, T., Vélez, W., Santana, E., Araújo, T., Mendonça, F., & Portela, A. (2019). A local mesh free method for linear elasticity and fracture mechanics. Engineering Analysis with Boundary Elements, 101, 221-242.
Ramalho, L. D. C., Belinha, J., & Campilho, R. D. S. G. (2019). The numerical simulation of crack propagation using radial point interpolation meshless methods. Engineering Analysis with Boundary Elements, 109, 187-198.
Shojaee, S., & Daneshmand, A. (2015). Crack analysis in media with orthotropic Functionally Graded Materials using extended Isogeometric analysis. Engineering Fracture Mechanics, 147, 203-227.
Srawley, J. E. (1976). Wide range stress intensity factor expressions for ASTM E 399 standard fracture toughness specimens. International Journal of Fracture, 12(3), 475-476.
Sun, Y., Hu, Y. G., & Liew, K. M. (2007). A mesh-free simulation of cracking and failure using the cohesive segments method. International Journal of Engineering Science, 45(2), 541-553.
That-Hoang, L. T., Nguyen-Van, H., Chau-Dinh, T., & Huynh-Van, C. (2018). Enhancement to four-node quadrilateral plate elements by using cell-based smoothed strains and higher-order shear deformation theory for nonlinear analysis of composite structures. Journal of Sandwich Structures & Materials, 1099636218797982.
Ton-That, H. L., Nguyen-Van, H., & Chau-Dinh, T. (2019). An Improved Four-Node Element for Analysis of Composite Plate/Shell Structures Based on Twice Interpolation Strategy. International Journal of Computational Methods, 1950020.
Ton That, H. L., Nguyen-Van, H., & Chau-Dinh, T. (2020). Nonlinear Bending Analysis of Functionally Graded Plates Using SQ4T Elements based on Twice Interpolation Strategy. Journal of Applied and Computational Mechanics, 6(1), 125-136.
Trädegård, A., Nilsson, F., & Östlund, S. (1998). FEM-remeshing technique applied to crack growth problems. Computer Methods in Applied Mechanics and Engineering, 160(1), 115-131.
Wen, L., & Tian, R. (2016). Improved XFEM: Accurate and robust dynamic crack growth simulation. Computer Methods in Applied Mechanics and Engineering, 308, 256-285.
Wu, J., & Cai, Y. (2014). A partition of unity formulation referring to the NMM for multiple intersecting crack analysis. Theoretical and Applied Fracture Mechanics, 72, 28-36.
Yin, S., Yu, T., Bui, T. Q., Zheng, X., & Gu, S. (2019). Static and dynamic fracture analysis in elastic solids using a multiscale extended isogeometric analysis. Engineering Fracture Mechanics, 207, 109-130.
Zheng, C., Wu, S. C., Tang, X. H., & Zhang, J. H. (2010). A novel twice-interpolation finite element method for solid mechanics problems. Acta Mechanica Sinica, 26(2), 265-278.
Anderssohn, R., Hofmann, M., & Bahr, H. A. (2018). FEM-bifurcation analysis for 3D crack patterns. Engineering Fracture Mechanics, 202, 363-374.
Barsoum, R. S. (1974). Application of quadratic isoparametric finite elements in linear fracture mechanics. International Journal of Fracture, 10(4), 603-605.
Bathe, K.-J. (2006). Finite element procedures. USA: Prentice Hall, Pearson Education, Inc.
Bergara, A., Dorado, J. I., Martin-Meizoso, A., & Martínez-Esnaola, J. M. (2017). Fatigue crack propagation in complex stress fields: Experiments and numerical simulations using the Extended Finite Element Method (XFEM). International Journal of Fatigue, 103, 112-121.
Bhardwaj, G., Singh, I. V., & Mishra, B. K. (2013). Numerical Simulation of Plane Crack Problems Using Extended Isogeometric Analysis. Procedia Engineering, 64, 661-670.
Bui, T. Q. (2015a). Extended isogeometric dynamic and static fracture analysis for cracks in piezoelectric materials using NURBS. Computer Methods in Applied Mechanics and Engineering, 295(Supplement C), 470-509.
Bui, T. Q. (2015b). Extended isogeometric dynamic and static fracture analysis for cracks in piezoelectric materials using NURBS. Computer Methods in Applied Mechanics and Engineering, 295, 470-509.
Bui, T. Q., Do, T. V., Ton, L. H. T., Doan, D. H., Tanaka, S., Pham, D. T., . . . Hirose, S. (2016). On the high temperature mechanical behaviors analysis of heated functionally graded plates using FEM and a new third-order shear deformation plate theory. Composites Part B: Engineering, 92, 218-241.
Bui, T. Q., Vo, D. Q., Zhang, C., & Nguyen, D. D. (2014). A consecutive-interpolation quadrilateral element (CQ4): Formulation and applications. Finite Elements in Analysis and Design, 84, 14-31.
Chau-Dinh, T., Mai-Van, C., Zi, G., & Rabczuk, T. (2018). New kinematical constraints of cracked MITC4 shell elements based on the phantom-node method for fracture analysis. Engineering Fracture Mechanics, 199, 159-178.
Chau-Dinh, T., & Zi, G. (2011). A Phantom-Node Method for Predicting Residual Strength in Shell Structures with a Single Crack Based on a Crack Tip Opening Angle Criterion. Procedia Engineering, 14, 630-635.
Chau-Dinh, T., Zi, G., Lee, P.-S., Rabczuk, T., & Song, J.-H. (2012). Phantom-node method for shell models with arbitrary cracks. Computers & Structures, 92-93, 242-256.
Chen, H., Wang, Q., Liu, G. R., Wang, Y., & Sun, J. (2016). Simulation of thermoelastic crack problems using singular edge-based smoothed finite element method. International Journal of Mechanical Sciences, 115-116, 123-134.
Chen, L., Liu, G. R., Jiang, Y., Zeng, K., & Zhang, J. (2011). A singular edge-based smoothed finite element method (ES-FEM) for crack analyses in anisotropic media. Engineering Fracture Mechanics, 78(1), 85-109.
Denda, M., & Marante, M. E. (2004). Mixed mode BEM analysis of multiple curvilinear cracks in the general anisotropic solids by the crack tip singular element. International Journal of Solids and Structures, 41(5), 1473-1489.
Duan, J. B., Lei, Y. J., & Li, D. K. (2011). Fracture analysis of linear viscoelastic materials using triangular enriched crack tip elements. Finite Elements in Analysis and Design, 47(10), 1157-1168.
Ewalds, H., & Wanhill, R. (1989). Fracture Mechanics. New York: Edward Arnold.
Fawkes, A. J., Owen, D. R. J., & Luxmoore, A. R. (1979). An assessment of crack tip singularity models for use with isoparametric elements. Engineering Fracture Mechanics, 11(1), 143-159.
Feng, S. Z., & Li, W. (2018). An accurate and efficient algorithm for the simulation of fatigue crack growth based on XFEM and combined approximations. Applied Mathematical Modelling, 55, 600-615.
Gall, K., Sehitoglu, H., & Kadioglu, Y. (1996). FEM study of fatigue crack closure under double slip. Acta Materialia, 44(10), 3955-3965.
Giner, E., Sukumar, N., Tarancón, J. E., & Fuenmayor, F. J. (2009). An Abaqus implementation of the extended finite element method. Engineering Fracture Mechanics, 76(3), 347-368.
Henshell, R. D., & Shaw, K. G. (1975). Crack tip finite elements are unnecessary. International Journal for Numerical Methods in Engineering, 9(3), 495-507.
Hu, X., Bui, T. Q., Wang, J., Yao, W., Ton, L. H. T., Singh, I. V., & Tanaka, S. (2017). A new cohesive crack tip symplectic analytical singular element involving plastic zone length for fatigue crack growth prediction under variable amplitude cyclic loading. European Journal of Mechanics - A/Solids, 65, 79-90.
Jayaswal, K., & Grosse, I. R. (1993). Finite element error estimation for crack tip singular elements. Finite Elements in Analysis and Design, 14(1), 17-35.
Kang, Z., Bui, T. Q., Nguyen, D. D., Saitoh, T., & Hirose, S. (2015). An extended consecutive-interpolation quadrilateral element (XCQ4) applied to linear elastic fracture mechanics. Acta Mechanica, 226(12), 3991-4015.
Kumar, S., Singh, I. V., & Mishra, B. K. (2015). A homogenized XFEM approach to simulate fatigue crack growth problems. Computers & Structures, 150(Supplement C), 1-22.
Kuna, M. (2013). Finite Elements in Fracture Mechanics: Theory - Numerics - Applications: Springer Science & Business Media.
Kwon, Y. W., & Akin, J. E. (1989). Development of a derivative singular element for application to crack propagation problems. Computers & Structures, 31(3), 467-471.
Liu, P., Bui, T. Q., Zhang, C., Yu, T. T., Liu, G. R., & Golub, M. V. (2012). The singular edge-based smoothed finite element method for stationary dynamic crack problems in 2D elastic solids. Computer Methods in Applied Mechanics and Engineering, 233-236(Supplement C), 68-80.
Moës, 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.
Nash Gifford, L., & Hilton, P. D. (1978). Stress intensity factors by enriched finite elements. Engineering Fracture Mechanics, 10(3), 485-496.
Nguyen-Van, H., Ton-That, H. L., Chau-Dinh, T., & Dao, N. D. (2018). Nonlinear Static Bending Analysis of Functionally Graded Plates Using MISQ24 Elements with Drilling Rotations. Paper presented at the Proceedings of the International Conference on Advances in Computational Mechanics 2017, Singapore.
Nguyen-Xuan, H., Liu, G. R., Nourbakhshnia, N., & Chen, L. (2012). A novel singular ES-FEM for crack growth simulation. Engineering Fracture Mechanics, 84, 41-66.
Olgierd Cecil Zienkiewicz, Kenneth Morgan, & Morgan, K. (2006). Finite elements and approximation: Courier Corporation.
Olgierd Cecil Zienkiewicz, Robert L Taylor, Perumal Nithiarasu, & Zhu, J. (1977). The finite element method: McGraw-hill.
Oliva, V., Cséplö, L., Materna, A., & Bláhová, L. (1997). FEM simulation of fatigue crack growth. Materials Science and Engineering: A, 234-236, 517-520.
Oliveira, T., Vélez, W., Santana, E., Araújo, T., Mendonça, F., & Portela, A. (2019). A local mesh free method for linear elasticity and fracture mechanics. Engineering Analysis with Boundary Elements, 101, 221-242.
Ramalho, L. D. C., Belinha, J., & Campilho, R. D. S. G. (2019). The numerical simulation of crack propagation using radial point interpolation meshless methods. Engineering Analysis with Boundary Elements, 109, 187-198.
Shojaee, S., & Daneshmand, A. (2015). Crack analysis in media with orthotropic Functionally Graded Materials using extended Isogeometric analysis. Engineering Fracture Mechanics, 147, 203-227.
Srawley, J. E. (1976). Wide range stress intensity factor expressions for ASTM E 399 standard fracture toughness specimens. International Journal of Fracture, 12(3), 475-476.
Sun, Y., Hu, Y. G., & Liew, K. M. (2007). A mesh-free simulation of cracking and failure using the cohesive segments method. International Journal of Engineering Science, 45(2), 541-553.
That-Hoang, L. T., Nguyen-Van, H., Chau-Dinh, T., & Huynh-Van, C. (2018). Enhancement to four-node quadrilateral plate elements by using cell-based smoothed strains and higher-order shear deformation theory for nonlinear analysis of composite structures. Journal of Sandwich Structures & Materials, 1099636218797982.
Ton-That, H. L., Nguyen-Van, H., & Chau-Dinh, T. (2019). An Improved Four-Node Element for Analysis of Composite Plate/Shell Structures Based on Twice Interpolation Strategy. International Journal of Computational Methods, 1950020.
Ton That, H. L., Nguyen-Van, H., & Chau-Dinh, T. (2020). Nonlinear Bending Analysis of Functionally Graded Plates Using SQ4T Elements based on Twice Interpolation Strategy. Journal of Applied and Computational Mechanics, 6(1), 125-136.
Trädegård, A., Nilsson, F., & Östlund, S. (1998). FEM-remeshing technique applied to crack growth problems. Computer Methods in Applied Mechanics and Engineering, 160(1), 115-131.
Wen, L., & Tian, R. (2016). Improved XFEM: Accurate and robust dynamic crack growth simulation. Computer Methods in Applied Mechanics and Engineering, 308, 256-285.
Wu, J., & Cai, Y. (2014). A partition of unity formulation referring to the NMM for multiple intersecting crack analysis. Theoretical and Applied Fracture Mechanics, 72, 28-36.
Yin, S., Yu, T., Bui, T. Q., Zheng, X., & Gu, S. (2019). Static and dynamic fracture analysis in elastic solids using a multiscale extended isogeometric analysis. Engineering Fracture Mechanics, 207, 109-130.
Zheng, C., Wu, S. C., Tang, X. H., & Zhang, J. H. (2010). A novel twice-interpolation finite element method for solid mechanics problems. Acta Mechanica Sinica, 26(2), 265-278.