| [1] |
Reddy, J. N.; Gartling, D. K., The finite element method in heat transfer and fluid dynamics[M] (2010), CRC Press · Zbl 1257.80001 |
| [2] |
Wrobel, L. C.; Brebbia, C. A., The boundary element method for steady state and transient heat conduction, Numer. Methods Therm. Probl., 58-73 (1979) · Zbl 0457.65074 |
| [3] |
Tan, F.; Liang, J. W.; Jiao, Y. Y., The BEM based on conformal Duffy-distance transformation for three-dimensional elasticity problems, Sci. China Technol. Sci., 63, 12, 2575-2583 (2020) |
| [4] |
Belytschko, T.; Lu, Y. Y.; Gu, L., Element-free Galerkin methods, Int. J. Numer. Methods Eng., 37, 2, 229-256 (1994) · Zbl 0796.73077 |
| [5] |
Bruch, J. C.; Zyvoloski, G., Transient two-dimensional heat conduction problems solved by the finite element method, Int. J. Numer. Methods Eng., 8, 3, 481-494 (1974) · Zbl 0281.65060 |
| [6] |
Bazyar, M. H.; Talebi, A., Scaled boundary finite-element method for solving non-homogeneous anisotropic heat conduction problems, Appl. Math. Model., 39, 23-24, 7583-7599 (2015) · Zbl 1443.80001 |
| [7] |
Cui, X. Y.; Li, Z. C.; Feng, H., Steady and transient heat transfer analysis using a stable node-based smoothed finite element method, Int. J. Therm. Sci., 110, 12-25 (2016) |
| [8] |
Sutradhar, A.; Paulino, G. H.; Gray, L. J., Transient heat conduction in homogeneous and non-homogeneous materials by the Laplace transform Galerkin boundary element method, Eng. Anal. Bound. Elem., 26, 2, 119-132 (2002) · Zbl 0995.80010 |
| [9] |
Sladek, J.; Sladek, V.; Tan, C. L., Analysis of transient heat conduction in 3D anisotropic functionally graded solids, by the MLPG method, Compt. Model. Eng. Sci., 32, 3, 161-174 (2008) · Zbl 1232.80006 |
| [10] |
Shi, G. H., Manifold method of material analysis[C], (Proceedings of the Transactions of the 9th Army Conference On Applied Mathematics and Computing. Proceedings of the Transactions of the 9th Army Conference On Applied Mathematics and Computing, Minneapolis, Minnesota (1991)), 57-76 |
| [11] |
Luo, S. M.; Zhang, X. W.; Cai, Y. C., The variational principle and application of numerical manifold method, Appl. Math. Mech., 22, 6, 658-663 (2001) · Zbl 1136.74396 |
| [12] |
Chiou, Y. J.; Lee, Y. M.; Tsay, R. J., Mixed mode fracture propagation by manifold method, Int. J. Fract., 114, 4, 327-347 (2004) |
| [13] |
Li, S.; Cheng, Y.; Wu, Y. F., Numerical manifold method based on the method of weighted residuals, Comput. Mech., 35, 6, 470-480 (2005) · Zbl 1109.74373 |
| [14] |
Jiang, Q.; Zhou, C.; Li, D., A three-dimensional numerical manifold method based on tetrahedral meshes, Comput. Struct., 87, 13-14, 880-889 (2009) |
| [15] |
Ma, G.; An, X.; He, L., The numerical manifold method: a review, Int. J. Comput. Methods, 7, 01, 1-32 (2010) · Zbl 1267.74129 |
| [16] |
Cai, Y.; Zhuang, X.; Zhu, H., A generalized and efficient method for finite cover generation in the numerical manifold method, Int. J. Comput. Methods, 10, 5, Article 1350028 pp. (2013) · Zbl 1359.65283 |
| [17] |
Huo, F.; He, S.; Jiang, Z., A high-order numerical manifold method with nine-node triangular meshes, Eng. Anal. Bound. Elem., 61, 172-182 (2015) · Zbl 1403.65133 |
| [18] |
Yang, Y.; Sun, G.; Zheng, H., A four-node quadrilateral element fitted to numerical manifold method with continuous nodal stress for crack analysis, Comput. Struct., 177, 69-82 (2016) |
| [19] |
Wen, W. B.; Yao, K.; Lei, H. S., A high-order numerical manifold method based on B-spline interpolation and its application in structural dynamics, Int. J. Appl. Mech., 8, 8, Article 1650093 pp. (2016) |
| [20] |
Tan, F.; Jiao, Y. Y., The combination of the boundary element method and the numerical manifold method for potential problems, Eng. Anal. Bound. Elem., 74, 19-23 (2017) · Zbl 1403.65230 |
| [21] |
Liu, F.; Xia, K., Structured mesh refinement in MLS-based numerical manifold method and its application to crack problems, Eng. Anal. Bound. Elem., 84, 42-51 (2017) · Zbl 1403.74085 |
| [22] |
Zheng, H.; Yang, Y., On generation of lumped mass matrices in partition of unity based methods, Int. J. Numer. Methods Eng., 112, 8, 1040-1069 (2017) · Zbl 07867242 |
| [23] |
Ma, G. W.; An, X. M.; Zhang, H. H., Modeling complex crack problems using the numerical manifold method, Int. J. Fract., 156, 1, 21-35 (2009) · Zbl 1273.74461 |
| [24] |
Wu, Z.; Wong, L. N.Y., Investigating the effects of micro-defects on the dynamic properties of rock using numerical manifold method, Constr. Build. Mater., 72, 72-82 (2014) |
| [25] |
Wong, L. N.Y.; Wu, Z., Application of the numerical manifold method to model progressive failure in rock slopes, Eng. Fract. Mech., 119, 1-20 (2014) |
| [26] |
Fan, L. F.; Yi, X. W.; Ma, G. W., Numerical manifold method (NMM) simulation of stress wave propagation through fractured rock mass, Int. J. Appl. Mech., 5, 02, Article 1350022 pp. (2013) |
| [27] |
Yang, S.; Ma, G.; Ren, X., Cover refinement of numerical manifold method for crack propagation simulation, Eng. Anal. Bound. Elem., 43, 37-49 (2014) · Zbl 1297.74169 |
| [28] |
He, J.; Liu, Q.; Wu, Z., Modelling transient heat conduction of granular materials by numerical manifold method, Eng. Anal. Bound. Elem., 86, 45-55 (2018) · Zbl 1403.80004 |
| [29] |
Wei, W.; Zhao, Q.; Jiang, Q., A new contact formulation for large frictional sliding and its implement in the explicit numerical manifold method, Rock Mech. Rock Eng., 53, 1, 435-451 (2020) |
| [30] |
Liu, Q.; Xu, X.; Wu, Z., A GPU-based numerical manifold method for modeling the formation of the excavation damaged zone in deep rock tunnels, Comput. Geotech., 118, 11, Article 103351 pp. (2020) |
| [31] |
Liang, J.; Tong, D.; Tan, F., Two-dimensional magnetotelluric modelling based on the numerical manifold method, Eng. Anal. Bound. Elem., 124, 87-97 (2021) · Zbl 1464.78013 |
| [32] |
Yang, Y.; Tang, X.; Zheng, H., Three-dimensional fracture propagation with numerical manifold method, Eng. Anal. Bound. Elem., 72, 65-77 (2016) · Zbl 1403.74091 |
| [33] |
Zhang, H. H.; Ma, G. W.; Fan, L. F., Thermal shock analysis of 2D cracked solids using the numerical manifold method and precise time integration, Eng. Anal. Bound. Elem., 75, 46-56 (2017) · Zbl 1403.74092 |
| [34] |
Wu, Z.; Wong, L. N.Y., Frictional crack initiation and propagation analysis using the numerical manifold method, Comput. Geotech., 39, 38-53 (2012) |
| [35] |
Liu, X.; Liu, Q.; Wei, L., Improved strength criterion and numerical manifold method for fracture initiation and propagation, Int. J. Geomech., 17, 5, Article E4016007 pp. (2017) |
| [36] |
Yang, Y.; Zheng, H., Direct approach to treatment of contact in numerical manifold method, Int. J. Geomech., 17, 5, Article E4016012 pp. (2017) |
| [37] |
Yang, Y.; Xu, D.; Zheng, H., Explicit discontinuous deformation analysis method with lumped mass matrix for highly discrete block system, Int. J. Geomech., 18, 9, Article 4018098 pp. (2018) |
| [38] |
Li, L. C.; Tang, C. A.; Wang, S. Y., A coupled thermo-hydrologic-mechanical damage model and associated application in a stability analysis on a rock pillar, Tunn. Undergr. Sp. Technol., 34, 38-53 (2013) |
| [39] |
Ekneligoda, T. C.; Marshall, A. M., A coupled thermal-mechanical numerical model of underground coal gasification (UCG) including spontaneous coal combustion and its effects, Int. J. Coal Geol., 199, 31-38 (2018) |
| [40] |
Sun, L.; Liu, Q.; Grasselli, G., Simulation of thermal cracking in anisotropic shale formations using the combined finite-discrete element method, Comput. Geotech., 117, Article 103237 pp. (2020) |
| [41] |
Wu, Z.; Zhou, Y.; Fan, L., A fracture aperture dependent thermal-cohesive coupled model for modelling thermal conduction in fractured rock mass, Comput. Geotech., 114, Article 103108 pp. (2019) |
