Citation: | Fan Liheng, Wang Dongdong, Liu Yuxiang, Du Honghui. A FINITE ELEMENT COLLOCATION METHOD WITH SMOOTHED NODAL GRADIENTS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(2): 467-481. DOI: 10.6052/0459-1879-20-361 |
[1] |
Zienkiewicz OC, Taylor RL, Zhu JZ. The Finite Element Method: Its Basis and Fundamentals. 7th Edition. Berlin: Elsevier, 2015
|
[2] |
田荣. C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 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
|
[1] | Li Zheng, Zhao Yuhao, Cui Haijian, Chen Mingfei. DYNAMIC BEHAVIOR OF ELASTIC BEAM SYSTEM COUPLED BY NONLINEAR ELEMENT WITH END[J]. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(10): 3023-3038. DOI: 10.6052/0459-1879-24-196 |
[2] | Gao Xiaowei, Liu Huayu, Cui Miao, Yang Kai, Lyu Jun, Peng Haifeng, Ruan Bo. GENERALIZED WEAK-FORM FREE ELEMENT METHOD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(9): 2741-2751. DOI: 10.6052/0459-1879-24-160 |
[3] | Like Deng, Dongdong Wang, Jiarui Wang, Junchao Wu. A GRADIENT SMOOTHING GALERKIN MESHFREE METHOD FOR THIN PLATE ANALYSIS WITH LINEAR BASIS FUNCTION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3): 690-702. DOI: 10.6052/0459-1879-19-004 |
[4] | Wang Siqiang, Ji Shunying. NON-LINEAR CONTACT MODEL FOR SUPER-QUADRIC ELEMENT CONSIDERING THE EQUIVALENT RADIUS OF CURVATURE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(5): 1081-1092. DOI: 10.6052/0459-1879-18-103 |
[5] | Tan Shujun, Hou Jian, Wu Zhigang, Du Jianming. THE PARAMETRIC VARATIONAL PRINCIPLE AND NON-LINEAR FINITE ELEMENT METHOD FOR ANALYSIS OF ASTROMESH ANTENNA STRUCTURES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(5): 770-775. DOI: 10.6052/0459-1879-14-126 |
[6] | Hu Dean, Han Xu, Xiao Yihua, Yang Gang. RESEARCH DEVELOPMENTS OF SMOOTHED PARTICLE HYDRODYNAMICS METHOD AND ITS COUPLING WITH FINITE ELEMENT METHOD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(5): 639-652. DOI: 10.6052/0459-1879-13-092 |
[7] | Junbo Zhang, Xikui Li. A mesh-free method based on linear complementary model for gradient plasticity continuum[J]. Chinese Journal of Theoretical and Applied Mechanics, 2009, 41(6): 888-897. DOI: 10.6052/0459-1879-2009-6-2008-376 |
[8] | Z.Y. Gao, Tongxi Yu, D. Karagiozova. Finite element simulation on the mechanical properties of MHS materials[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 23(1): 65-75. DOI: 10.6052/0459-1879-2007-1-2006-198 |
[9] | THE CONVERGENCE PROOF OF THE PLANE RATIONAL FINITE ELEMENT[J]. Chinese Journal of Theoretical and Applied Mechanics, 1997, 29(6): 676-685. DOI: 10.6052/0459-1879-1997-6-1995-284 |
[10] | LOCAL ARC-LENGTH METHOD——A SOLUTION PROCEDURE FOR NON-LINEAR FINITE ELEMENT METHOD[J]. Chinese Journal of Theoretical and Applied Mechanics, 1997, 29(1): 116-122. DOI: 10.6052/0459-1879-1997-1-1995-205 |
1. |
齐栋梁. 超收敛光滑再生梯度无网格配点法. 力学与实践. 2024(04): 820-829 .
![]() | |
2. |
刘华雩,高效伟,范伟龙. 分区有限线法及其在复合结构热应力分析中的应用. 力学学报. 2023(06): 1394-1406 .
![]() | |
3. |
周东谟,王辉,惠步青,吴晗旭,陈航. 基于梯度有限元法的HTPB推进剂药柱结构完整性分析. 固体火箭技术. 2023(05): 695-707 .
![]() | |
4. |
胡凯,高效伟,徐兵兵,郑颖人. 多孔介质弹性问题的单元微分法. 岩土工程学报. 2023(11): 2403-2410 .
![]() | |
5. |
胡凯,高效伟,徐兵兵. 求解固体力学问题的强-弱耦合形式单元微分法. 力学学报. 2022(07): 2050-2058 .
![]() | |
6. |
傅卓佳,李明娟,习强,徐文志,刘庆国. 物理信息依赖核函数配点法的研究进展. 力学学报. 2022(12): 3352-3365 .
![]() |