[1] |
Zienkiewicz OC, Taylor RL, Zhu JZ. The Finite Element Method: Its Basis and Fundamentals. 7th Edition. Berlin: Elsevier, 2015
|
[2] |
田荣. C$^{1}$连续型广义有限元格式. 力学学报, 2019,51(1):263-277(Tian Rong. A GFEM with C$^{1}$ continuity. Chinese Journal of Theoretical and Applied Mechanics. 2019,51(1):263-277 (in Chinese))
|
[3] |
张雄, 刘岩, 马上. 无网格法的理论与应用. 力学进展, 2009,39(1):1-36(Zhang Xiong, Liu Yan, Ma Shang. Meshfere methods and their applications. Advances in Mechanics. 2009,39(1):1-36 (in Chinese))
|
[4] |
Chen JS, Hillman M, Chi SW. Meshfree methods: progress made after 20 years. Journal of Engineering Mechanics-ASCE, 2017,143(4):04017001
|
[5] |
Wang DD, Wu JC. An inherently consistent reproducing kernel gradient smoothing framework toward efficient Galerkin meshfree formulation with explicit quadrature. Computer Methods in Applied Mechanics and Engineering, 2019,349:628-672
|
[6] |
Hughes TJR, Cottrell JA, Bazilevs Y. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer Methods in Applied Mechanics and Engineering, 2005,194:4135-4195
|
[7] |
Zhang HJ, Wang DD. Reproducing kernel formulation of B-spline and NURBS basis functions: A meshfree local refinement strategy for isogeometric analysis. Computer Methods in Applied Mechanics and Engineering, 2017,320:474-508
|
[8] |
Kansa EJ. Multiquadrics-A scattered data approximation scheme with applications to computational fluid-dynamics-II solutions to parabolic, hyperbolic and elliptic partial differential equations. Computers & Mathematics with Applications, 1990,19(8-9):147-161
|
[9] |
Zhang X, Song KZ, Lu MW. et al. Meshless methods based on collocation with radial basis functions. Computational Mechanics, 2000,26(4):333-343
|
[10] |
Chen W. A meshless, integration-free, and boundary-only RBF technique. Computers & Mathematics with Applications, 2002,43(3-5):379-391
|
[11] |
Chen JS, Hu W, Hu H. Reproducing kernel enhanced local radial basis collocation method. International Journal for Numerical Methods in Engineering, 2008,75:600-627
|
[12] |
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):743-753(Wang Lihua, Li Yiming, Zhu 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))
|
[13] |
Mountris KA, Pueyo E. The radial point interpolation mixed collocation method for the solution of transient diffusion problems. Engineering Analysis with Boundary Elements, 2020,121:207-216
|
[14] |
Breitkopf P, Touzot G, Villon P. Double grid diffuse collocation method. Computational Mechanics, 2000,25(2):199-206
|
[15] |
Aluru NR. A point collocation method based on reproducing kernel approximations. International Journal for Numerical Methods in Engineering, 2015,47(6):1083-1121
|
[16] |
Chi SW, Chen JS, Hu HY. et al. A gradient reproducing kernel collocation method for boundary value problems. International Journal for Numerical Methods in Engineering, 2013,93:1381-1402
|
[17] |
Mahdavi A, Chi SW, Zhu HQ. A gradient reproducing kernel collocation method for high order differential equations. Computational Mechanics, 2019,64:1421-1454
|
[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
|
[19] |
Auricchio F, Beir?o L, Veiga D. et al. Isogeometric collocation methods. Mathematical Models and Methods in Applied Sciences, 2010,20:2075-2107
|
[20] |
Maurin F, Greco F, Coox L. et al. Isogeometric collocation for Kirchhoff-Love plates and shells. Computer Methods in Applied Mechanics & Engineering, 2018,328:396-420
|
[21] |
Kapl M, Vitrih V. Isogeometric collocation on planar multi-patch domains. Computer Methods in Applied Mechanics and Engineering, 2020,360:112684
|
[22] |
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))
|
[23] |
Gao XW, Gao L, 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
|
[24] |
Wang DD, Wang JR, Wu JC. Superconvergent gradient smoothing meshfree collocation method. Computer Methods in Applied Mechanics and Engineering, 2018,340:728-766
|
[25] |
Wang DD, Wang JR, Wu JC. Arbitrary order recursive formulation of meshfree gradients with application to superconvergent collocation analysis of Kirchhoff plates. Computational Mechanics, 2020,65:877-903.
|
[26] |
Qi DL, Wang DD, Deng LK, et al. Reproducing kernel meshfree collocation analysis of structural vibrations. Engineering Computations, 2019,36(3):734-764
|
[27] |
邓立克, 王东东, 王家睿 等. 薄板分析的线性基梯度光滑伽辽金无网格法. 力学学报, 2019,51(3):688-702(Deng Like, Wang Dongdong, Wang Jiarui, et al. A gradient smoothing Galerkin method for thin plate analysis with linear basis function. Chinese Journal of Theoretical and Applied Mechanics. 2019,51(3):690-792 (in Chinese))
|
[28] |
Chen JS, Wu CT, Yoon S. et al. A stabilized conforming nodal integration for Galerkin meshfree methods. International Journal for Numerical Methods in Engineering, 2001,50:435-466
|
[29] |
Liu GR, Dai KY, Nguyen TT. A smoothed finite element method for mechanics problems. Computational Mechanics, 2007,39:859-877
|
[30] |
Idesman A, Dey B. The use of the local truncation error for the increase in accuracy of the linear finite elements for heat transfer problems. Computer Methods in Applied Mechanics and Engineering, 2017,319:52-82
|