[1] 林绍忠, 明峥嵘, 祁勇峰. 用数值流形法分析温度场及温度应力[J]. 长江科学院院报, 2007, 24(5): 72-75 (LIN Shao-zhong, MING Zheng-rong, QI Yong-feng. Thermal Field and Thermal Stress Analysis Based On Numerical Manifold Method[J]. Journal of Yangtze River Scientific Research Institute, 2007, 24(5): 72-75. (in Chinese)).
[2] 任继勋, 佳琳, 阳建新, 等. 渗流条件下地下水含盐量对基坑坑底冻结温度场影响的数值模拟[J]. 长江科学院院报, 2024, 41(1): 151-158, 166.
(REN Ji-xun, JIA Lin, YANG Jian-xin, et al.Numerical Simulation On the Effect of Groundwater Salinity On Freezing Temperature Field at the Bottom of Foundation Pit Under Seepage Conditions[J]. Journal of Yangtze River Scientific Research Institute, 2024, 41(1): 151-158, 166. (in Chinese))
[3] 郭平业, 卜墨华, 张鹏, 等. 高地温隧道灾变机制与灾害防控研究进展[J]. 岩石力学与工程学报, 2023, 42(7): 1561-1581.
(GUO Ping-ye, BU Mo-hua, ZHANG Peng, et al.Review On Catastrophe Mechanism and Disaster Countermeasure of High Geotemperature Tunnels[J]. Chinese Journal of Rock Mechanics and Engineering, 2023, 42(7): 1561-1581. (in Chinese))
[4] 江文豪, 冯晨, 李江山. 饱和黏土一维非线性固结与热传导耦合模型[J]. 岩石力学与工程学报, 2023, 42(10): 2588-2600.
(JIANG Wen-hao, Feng Chen, LI Jiang-shan.Coupled Model for One-Dimensional Nonlinear Consolidation and Heat Conduction in Saturated Clay[J]. Chinese Journal of Rock Mechanics and Engineering, 2023, 42(10): 2588-2600. (in Chinese))
[5] 史策. 热传导方程有限差分法的Matlab实现[J]. 咸阳师范学院学报, 2009, 24(4): 27-29, 36.
(SHI Ce.Heat Conduction Equation Finite Difference Method to Achieve the Matlab[J]. Journal of Xianyang Normal University, 2009, 24(4): 27-29, 36. (in Chinese))
[6] Annasabi Z, Erchiqui F.Robust Kirchhoff Transformation Using B-Spline for Finite Element Analysis of the Non-Linear Heat Conduction[J]. International Communications in Heat and Mass Transfer, 2021, 120: 104985.
[7] Feng W, Gao X.An Interface Integral Equation Method for Solving Transient Heat Conduction in Multi-Medium Materials with Variable Thermal Properties[J]. International Journal of Heat and Mass Transfer, 2016, 98: 227-239.
[8] 王峰, 林皋, 郑保敬, 等. 非线性热传导问题的基于滑动Kriging插值的MLPG法[J]. 大连理工大学学报, 2014, 54(3): 339-344.
(WANG Feng, LIN Gao, ZHENG Baojing, et al.MLPG method based on moving Kriging interpolation for solving nonlinear heat conduction problems[J]. Journal of Dalian University of Technology. 2014(3): 339-344. (in Chinese))
[9] 吴泽艳, 郑保敬, 叶永, 等. 非线性热传导方程无网格MLPG/RBF-FD数值模拟[J]. 工程热物理学报, 2022, 43(1): 164-172.
(Wu Ze-yan, Zheng Bao-jing, Ye Yong, et al.Numerical simulation for the nonlinear heat conduction equations based on MLPG/RBF-FD meshless method[J]. 2022, 43(1): 164-172. (in Chinese))
[10] 李庆华, 冯子超, 陈莘莘, 等. 稳态非线性热传导问题的比例边界有限元法[J]. 华东交通大学学报, 2023, 40(6): 110-114.
(Li Qing-hua, Feng Zi-chao, Chen Shen-shen, et al.Scaled Boundary Finite Element Method for steady-state nonlinear heat conduction problem[J]. Journal of East China Jiaotong University. 2023, 40(6): 110-114. (in Chinese))
[11] Zhang L, Guo F, Zheng H.The MLS-Based Numerical Manifold Method for Nonlinear Transient Heat Conduction Problems in Functionally Graded Materials[J]. International Communications in Heat and Mass Transfer, 2022, 139: 106428.
[12] 李腊梅, 冯春. 一种非连续介质中热传导过程的数值模拟方法[J]. 工程力学, 2016, 33(1): 25-31, 46.
(LI La-mei, FENG Chun.A numerical simulation method for heat conduction in discontinuous media[J]. Engineering Mechanics. 2016, 33(1): 25-31, 46. (in Chinese))
[13] 刘承论, 秦忠诚. 三维非稳态热传导问题的边界元法[J]. 岩石力学与工程学报, 2004, 23(18): 3168-3173.
(Liu Cheng-lun, Qin Zhong-cheng.Boundary element method for 3D Non-steady heat conduction[J]. Chinese Journal of Rock Mechanics and Engineering. 2004, 23(18): 3168-3173. (in Chinese))
[14] 梁钰, 郑保敬, 高效伟, 等. 基于Pod模型降阶法的非线性瞬态热传导分析[J]. 中国科学(物理学力学天文学), 2018, 48(12): 32-41.
(LIANG Yu, ZHENG Bao-Jing, GAO Xiao-wei, et al.Reduced order model analysis method via proper orthogonal decomposition for nonlinear transient heat conduction problems[J]. SCIENTIA SINICA Physica, Mechanica & Astronomica. 2018, 48(12): 32-41. (in Chinese))
[15] Suvin V S, Ooi E T, Song C, et al.Temperature-Dependent Nonlinear Transient Heat Conduction Using the Scaled Boundary Finite Element Method[J]. International Journal of Heat and Mass Transfer, 2025, 243: 126780.
[16] Mierzwiczak M, Chen W, Fu Z.The Singular Boundary Method for Steady-State Nonlinear Heat Conduction Problem with Temperature-Dependent Thermal Conductivity[J]. International Journal of Heat and Mass Transfer, 2015, 91: 205-217.
[17] Yang K, Feng W, Wang J, et al.Ribem for 2D and 3D Nonlinear Heat Conduction with Temperature Dependent Conductivity[J]. Engineering Analysis with Boundary Elements, 2018, 87: 1-8.
[18] Khosravifard A, Hematiyan M R, Marin L.Nonlinear Transient Heat Conduction Analysis of Functionally Graded Materials in the Presence of Heat Sources Using an Improved Meshless Radial Point Interpolation Method[J]. Applied Mathematical Modelling, 2011, 35(9): 4157-4174.
[19] Shi G H.Manifold Method of Material Analysis[C]//. Transactions of the 9 Army Conference On Applied Mathematics and Computing, 1991.
[20] Zhang L, Kong H, Zheng H.Numerical Manifold Method for Steady-State Nonlinear Heat Conduction Using Kirchhoff Transformation[J]. Science China Technological Sciences, 2023, 67(4): 992-1006.
[21] 贾真, 杨冬梅, 郑宏. 数值流形法渗流分析中处理弱不连续界面的新方法[J]. 长江科学院院报, 2023: 1-7.
(JIA Zhen, YANG Dong-mei, Zheng Hong.A New Method to Deal with Weak Discontinuous Interface in Seepage Analysis Based On Numerical Manifold Method[J]. Journal of Yangtze River Scientific Research Institute, 2023: 1-7. (in Chinese))
[22] 李伟, 郑宏, 王海龙, 等. 求解断裂问题的新型无网格数值流形法[J]. 岩石力学与工程学报, 2020, 39(S1): 2655-2664.
(Li Wei, Zheng Hong, Wang Hai-long, et al.A new meshfree-numerical manifold method for solving the fracture problem[J]. 2020, 39(S1): 2655-2664. (in Chinese))
[23] 王方义, 郑宏. 无界域问题的数值流形法[J]. 长江科学院院报, 2023, 40(7): 110-117.
(WANG Fang-yi, Zheng Hong.Numerical Manifold Method for Unbounded Domain Problems[J]. Journal of Yangtze River Scientific Research Institute, 2023, 40(7): 110-117. (in Chinese))
[24] 陈远强, 郑宏, 陈涛. 基于数值流形法的重力坝抗滑稳定性分析[J]. 长江科学院院报, 2016, 33(9): 133-137.
(CHEN Yuan-qiang, Zheng Hong, Chen Tao.Analysis of Anti-Sliding Stability of Gravity Dam Using Numerical Manifold Method[J]. Journal of Yangtze River Scientific Research Institute, 2016, 33(9): 133-137. (in Chinese))
[25] 胡国栋, 张慧华, 谭育新. 功能梯度材料稳态热传导问题的数值流形方法研究[J]. 应用力学学报, 2017, 34(2): 311-317.
(Hu Guo-dong, Zhang Hui-hua, Tan Yu-xin.Numerical manifold study of steady heat conduction problems in functionally graded materials[J]. Chinese Journal of Applied Mechanics. 2017, 34(2): 311-317. (in Chinese))
[26] Tan F, Tong D, Liang J, et al.Two-Dimensional Numerical Manifold Method for Heat Conduction Problems[J]. Engineering Analysis with Boundary Elements, 2022, 137: 119-138.
[27] Wang K, Tang C A, Qian X, et al.Numerical Manifold Method with Local Mesh Refinement for Thermo-Mechanical Coupling Analysis in Rocks[J]. Computers and Geotechnics, 2025, 179: 107009.
[28] Li C L, Guo D L, Zhang H H.The Numerical Manifold Method for Piezoelectric Materials with Hole Flaws Under Electro-Mechanical Loadings[J]. Engineering Analysis with Boundary Elements, 2025, 173: 106149.
[29] Zhang Y, Zheng H, Lin S.Random Structure Modeling of Soil and Rock Mixture and Evaluation of its Permeability Using Three-Dimensional Numerical Manifold Method[J]. Computers and Geotechnics, 2025, 180: 107089.
[30] 苏海东, 颉志强, 龚亚琦, 等. 基于独立覆盖的流形法的收敛性及覆盖网格特性[J]. 长江科学院院报, 2016, 33(2): 131-136.
(SU Hai-dong, XIE Zhi-qiang, GONG Ya-qi, et al.Characteristics of Convergence and Cover Mesh in Numerical Manifold Method Based On Independent Covers[J]. Journal of Yangtze River Scientific Research Institute, 2016, 33(2): 131-136. (in Chinese))
[31] Wu W, Wan T, Yang Y, et al.Three-Dimensional Numerical Manifold Formulation with Continuous Nodal Gradients for Dynamics of Elasto-Plastic Porous Media[J]. Computer Methods in Applied Mechanics and Engineering, 2022, 388: 114203.
[32] Zheng H, Liu F, Li C.The Mls-Based Numerical Manifold Method with Applications to Crack Analysis[J]. International Journal of Fracture, 2014, 190(1-2): 147-166.
[33] Mengsu H, Yuan W, Rutqvist J.On Continuous and Discontinuous Approaches for Modeling Groundwater Flow in Heterogeneous Media Using the Numerical Manifold Method; Model Development and Comparison[J]. Advances in Water Resources, 2015, 80(C): 17-29.
[34] Zheng H, Li W, Du X.Exact Imposition of Essential Boundary Condition and Material Interface Continuity in Galerkin‐Based Meshless Methods[J]. International Journal for Numerical Methods in Engineering, 2017, 110(7): 637-660.
[35] Yang K, Wang J, Du J, et al.Radial Integration Boundary Element Method for Nonlinear Heat Conduction Problems with Temperature-Dependent Conductivity[J]. International Journal of Heat and Mass Transfer, 2017, 104: 1145-1151.
[36] Zhang L, Yin Y, Zheng H, et al.Singularity Treatments in Transient Confined Seepage Using Numerical Manifold Method[J]. Engineering Analysis with Boundary Elements, 2025, 171: 106100.
[37] Yang K, Li H, Peng H, et al.New Interface Integration Bem for Solving Multi-Medium Nonlinear Heat Transfer Problems[J]. Engineering Analysis with Boundary Elements, 2020, 117: 66-75.
