[1] |
Qin X, Shen YJ, Chen W, et al. Bending and free vibration analyses of circular stiffened plates using the FSDT mesh-free method. International Journal of Mechanical Sciences, 2021, 202: 106498
|
[2] |
Chen JS, Hillman M, Chi SW. Meshfree methods: progress made after 20 years. Journal of Engineering Mechanics, 2017, 143(4): 04017001 doi: 10.1061/(ASCE)EM.1943-7889.0001176
|
[3] |
张雄, 刘岩. 无网格法. 北京: 清华大学出版社有限公司, 2004Zhang Xiong, Liu Yan. Meshless Methods. Beijing: Tsinghua University Press, 2004 (in Chinese))
|
[4] |
陈健, 王东东, 刘宇翔等. 无网格动力分析的循环卷积神经网络代理模型. 力学学报, 2022, 54: 1-14 (Chen Jian, Wang Dongdong, Liu Yuxiang, et al. A recurrent convolutional neural network surrogate model for dynamic meshfree analysis. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54: 1-14 (in Chinese) doi: 10.6052/0459-1879-17-020
|
[5] |
Zhang X, Song KZ, Lu MW, et al. Meshless methods based on collocation with radial basis functions. Computational Mechanics, 2000, 26(4): 333-343 doi: 10.1007/s004660000181
|
[6] |
Huang TH. Stabilized and variationally consistent integrated meshfree formulation for advection-dominated problems. Computer Methods in Applied Mechanics and Engineering, 2023, 403: 115698 doi: 10.1016/j.cma.2022.115698
|
[7] |
Li ML, Nikan O, Qiu WL, et al. An efficient localized meshless collocation method for the two-dimensional Burgers-type equation arising in fluid turbulent flows. Engineering Analysis with Boundary Elements, 2022, 144: 44-54 doi: 10.1016/j.enganabound.2022.08.007
|
[8] |
Wang DD, Wang JR, Wu JC. Superconvergent gradient smoothing meshfree collocation method. Computer Methods in Applied Mechanics and Engineering, 2018, 340: 728-766 doi: 10.1016/j.cma.2018.06.021
|
[9] |
王莉华, 阮剑武. 配点型无网格法理论和研究进展. 力学季刊, 2021, 42(4): 613Wang Lihua, Ruan Jianwu. Theory and research progress of collocation-type meshless method. Chinese Quarterly of Mechanics, 2021, 42(4): 613 (in Chinese))
|
[10] |
Li JC, Cheng AHD, Chen CS. A comparison of efficiency and error convergence of multiquadric collocation method and finite element method. Engineering Analysis with Boundary Elements, 2003, 27(3): 251-257 doi: 10.1016/S0955-7997(02)00081-4
|
[11] |
Wang LH, Liu YJ, Zhou YT, et al. Static and dynamic analysis of thin functionally graded shell with in-plane material inhomogeneity. International Journal of Mechanical Sciences, 2021, 193: 106165 doi: 10.1016/j.ijmecsci.2020.106165
|
[12] |
Hillman M, Chen JS. Performance comparison of nodally integrated Galerkin meshfree methods and nodally collocated strong form meshfree methods. Advances in Computational Plasticity, 2018: 145-164
|
[13] |
Zhang X, Liu XH, Song KZ, et al. Least-squares collocation meshless method. International Journal for Numerical Methods in Engineering, 2001, 51(9): 1089-1100 doi: 10.1002/nme.200
|
[14] |
Liu Y, Zhang X, Lu MW. Meshless least-squares method for solving the steady-state heat conduction equation. Tsinghua Science and Technology, 2005, 10(1): 61-66 doi: 10.1016/S1007-0214(05)70010-9
|
[15] |
Chen JS, Wang LH, Hu HY, et al. Subdomain radial basis collocation method for heterogeneous media. International Journal for Numerical Methods in Engineering, 2009, 80(2): 163-190 doi: 10.1002/nme.2624
|
[16] |
Wang LH, Chen JS, Hu HY. Subdomain radial basis collocation method for fracture mechanics. International Journal for Numerical Methods in Engineering, 2010, 83(7): 851-876 doi: 10.1002/nme.2860
|
[17] |
王莉华, 李溢铭, 褚福运. 基于分区径向基函数配点法的大变形分析. 力学学报, 2019, 51(3): 743-753Wang Lihua, Li Yiming, Chu Fuyun. Finite subdomain radial basis collocation method for the large deformation analysis. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3): 743-753 (in Chinese))
|
[18] |
Wang LH, Qian ZH. A meshfree stabilized collocation method (SCM) based on reproducing kernel approximation. Computer Methods in Applied Mechanics and Engineering, 2020, 371: 113303 doi: 10.1016/j.cma.2020.113303
|
[19] |
Qian ZH, Wang LH, Gu Y, et al. An efficient meshfree gradient smoothing collocation method (GSCM) using reproducing kernel approximation. Computer Methods in Applied Mechanics and Engineering, 2021, 374: 113573 doi: 10.1016/j.cma.2020.113573
|
[20] |
王莉华, 刘义嘉, 钟伟等. 无网格稳定配点法及其在弹性力学中的应用. 计算力学学报, 2021, 38(3): 305-312 (Wang Lihua, Liu Yijia, Zhong Wei, et al. Meshfree stabilized collocation method in elasticity. Chinese Journal of Computational Mechanics, 2021, 38(3): 305-312 (in Chinese)
|
[21] |
Belytschko T, Lu YY, Gu L. Element-free Galerkin methods. International Journal for Numerical Methods in Engineering, 1994, 37(2): 229-256 doi: 10.1002/nme.1620370205
|
[22] |
Zhu T, Atluri SN. A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method. Computational Mechanics, 1998, 21(3): 211-222 doi: 10.1007/s004660050296
|
[23] |
Liu DJ, Cheng YM. The interpolating element-free Galerkin (IEFG) method for three-dimensional potential problems. Engineering Analysis with Boundary Elements, 2019, 108: 115-123 doi: 10.1016/j.enganabound.2019.08.021
|
[24] |
Qian ZH, Wang LH, Zhang CZ, et al. A highly efficient and accurate Lagrangian–Eulerian stabilized collocation method (LESCM) for the fluid−rigid body interaction problems with free surface flow. Computer Methods in Applied Mechanics and Engineering, 2022, 398: 115238 doi: 10.1016/j.cma.2022.115238
|
[25] |
Gao XW, Huang SZ, Cui M, et al. Element differential method for solving general heat conduction problems. International Journal of Heat and Mass Transfer, 2017, 115: 882-894 doi: 10.1016/j.ijheatmasstransfer.2017.08.039
|
[26] |
Gao XW, Gao LF, Zhang Y, et al. Free element collocation method: A new method combining advantages of finite element and mesh free methods. Computers & Structures, 2019, 215: 10-26
|
[27] |
高效伟, 徐兵兵, 吕军等. 自由单元法及其在结构分析中的应用. 力学学报, 2019, 51(3): 703-713 (Gao Xiaowei, Xu Bingbing, Lü Jun, et al. Free element method and its application in structural analysis. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3): 703-713 (in Chinese)
|
[28] |
高效伟, 丁金兴, 刘华雩. 有限线法及其在流固域间耦合传热中的应用. 物理学报, 2022, 71(19): 190201 (Gao Xiaowei, Ding Jinxing, Liu Huayu. Finite line method and its application in coupled heat transfer between fluid-solid domains. Acta Physica Sinica, 2022, 71(19): 190201 (in Chinese) doi: 10.7498/aps.71.20220833
|
[29] |
Wang LH, Hu MH, Zhong Z, et al. Stabilized Lagrange interpolation collocation method: A meshfree method incorporating the advantages of finite element method. Computer Methods in Applied Mechanics and Engineering, 2023, 404: 115780 doi: 10.1016/j.cma.2022.115780
|
[30] |
Hu HY, Lai CK, Chen JS. A study on convergence and complexity of reproducing kernel collocation method. Interaction and Multiscale Mechanics, 2009, 2(3): 295-319
|