变节点余能原理基面力元法单元模型性能研究

王耀; 胥民尧; 纵岗; 侯长超

doi:10.21656/1000-0887.450059

变节点余能原理基面力元法单元模型性能研究

doi: 10.21656/1000-0887.450059

盐城工业职业技术学院建筑工程学院，江苏盐城 224005

基金项目:

2023年度国家外国专家项目(个人类)（G2023014042L）；江苏省外国专家工作室项目；江苏省高职院校教师访学研修项目（2024GRFX071）；江苏高校“青蓝工程”优秀青年骨干教师项目；江苏省高等学校自然科学研究A类项目（19KJB560006）

详细信息

作者简介:
王耀（1986—），男，副教授，博士(通讯作者. E-mail: yaowang@yctei.edu.cn).

通讯作者:
王耀（1986—），男，副教授，博士(通讯作者. E-mail: yaowang@yctei.edu.cn).

中图分类号: O343.1|O343.2
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- 文章访问数: 27
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- 被引次数: 0
出版历程
- 收稿日期: 2024-03-05
- 修回日期: 2024-05-04
- 网络出版日期: 2025-04-02
- 刊出日期: 2025-03-01

Performances of Variable-Node Elements With the Base Force Element Method Under the Complementary Energy Principle

School of Architecture and Engineering, Yancheng Polytechnic College, Yancheng, Jiangsu 224005, P.R.China

摘要

摘要: 为了解决疏密单元网格交界面节点位移不协调、求解方程构造复杂及空间可扩展性能差的问题，基于余能原理基面力元法提出了一种可变节点数量及位置的单元模型，并针对任意单元类型建立了一种具有统一形式的显式求解方法.首先，建立了一种二维可变边中节点单元模型，介绍了边中节点的柔度贡献矩阵及节点位移显式表达式；随后，将该模型扩展到三维层次，建立了一种可变面中节点单元模型，并将节点柔度贡献矩阵及节点位移表达式扩展到三维单元.基于上述模型，建立了平面及空间问题的疏密网格悬挂单元模型，并通过端部承受弯矩荷载、集中荷载及拉伸荷载的悬臂梁算例，论证了平面及空间可变节点单元模型、疏密网格悬挂单元模型的数值精度和适用性.研究表明，基于余能原理基面力元法建立的平面及空间可变节点单元模型具有较高的数值精度；此外，疏密网格之间的交界面无需进行任何处理措施，也无需构造插值函数或约束函数，仅依靠疏密网格交界面共用的边中节点(2D)及面中节点(3D)即可确保疏密网格交界面的节点位移协调；同时，模型和方法独立于单元类型、单元维度、节点数量及分布等因素，具有优异的空间可扩展性能及易于程序化的特点.
- 基面力元法 /
- 变节点单元 /
- 余能原理 /
- 悬挂单元模型
Abstract: To address the problems of uncoordinated nodal displacements at the intersection of the sparse and dense elements, complicated construction of solving equations, and poor spatial scalability, an element model with variable node numbers and positions was proposed with the base force element method (BFEM) under the complementary energy principle, and an explicit solution method in a unified form was established for arbitrary element types. First, a 2D variable mid-edge node element model was established, and the explicit expressions of the contribution of nodes compliance matrix and nodal displacements were introduced. Subsequently, the element model was extended to the 3D form, a variable mid-face node element model was proposed, and the above expressions were also extended to the 3D forms. Hereafter, a sparse and dense mesh hanging element model was established, and the numerical accuracy and applicability of the planar and spatial variable-node element model were demonstrated with the cantilever beam subjected to a bending moment load, a concentrated load, and a tensile load at the end. The numerical results show that, the variable-node element model and the hanging element model in the 2D and 3D forms based on the BFEM have high numerical accuracy. In addition, the nodal displacement coordination at the intersection interface between sparse and dense elements can be ensured only by the shared mid-edge node (2D) and the mid-face node (3D) at the interface without any processing treatment or construction of interpolation functions and constraint functions. Meanwhile, the element models and methods are independent of the element type, element dimensions, nodes’ number, and nodes’ distribution, etc., and have excellent spatial scalability and programmability.
- base force element method /
- variable-node element /
- complementary energy principle /
- hanging element model

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参考文献(24)

[2]LIM J H, SOHN D, IM S. Variable-node element families for mesh connection and adaptive mesh computation[J]. Structural Engineering and Mechanics,2012,43(3): 349-370.

钟红, 林皋, 陈健云. 一种用于有限元疏密过渡的新型十三节点单元[J]. 哈尔滨工业大学学报, 2009,41(4): 219-221.

(ZHONG Hong, LIN Gao, CHEN Jianyun. A thirteen-node element for transition between course and fine finite element meshes[J]. Journal of Harbin Institute of Technology,2009,41(4): 219-221. (in Chinese))

[3]TU T K, YU H F, RAMIREZ-GUZMAN L, et al. From mesh generation to scientific visualization: an end-to-end approach to parallel supercomputing[C]//SC’06: Proceedings of the 2006 ACM/IEEE Conference on Supercomputing. Tampa, FL, USA: IEEE, 2006: 12.

[4]HIRSHIKESH, PRAMOD A L N, OOI E T, et al. An adaptive scaled boundary finite element method for contact analysis[J]. European Journal of Mechanics A: Solids,2021,86: 104180.

[5]WIJESINGHE D R, DYSON A, YOU G, et al. Development of the scaled boundary finite element method for image-based slope stability analysis[J]. Computers and Geotechnics,2022,143: 104586.

[6]强天驰, 寇晓东, 周维垣. 三维有限元网格加密界面协调方法及在大坝开裂分析中的应用[J]. 岩石力学与工程学报, 2000,〖STHZ〗19(5): 562-566.(QIANG Tianchi, KOU Xiaodong, ZHOU Weiyuan. Three-dimensional fem interface coupled method and its application to arch dam fracture analysis[J]. Chinese Journal of Rock Mechanics and Engineering,2000,19(5): 562-566. (in Chinese))

[7]钟红, 林皋, 胡志强. 有限元计算中疏密网格过渡方法研究[J]. 计算力学学报, 2007,〖STHZ〗24(6): 887-891.(ZHONG Hong, LIN Gao, HU Zhiqiang. Two methods for transition between coarse and fine finite elements[J]. Chinese Journal of Computational Mechanics,2007,24(6): 887-891. (in Chinese))

[8]孙志刚, 宋迎东, 上官莉英, 等. 无虚拟节点的有限元界面协调技术[J]. 计算力学学报, 2005,〖STHZ〗22(3): 374-378.(SUN Zhigang, SONG Yingdong, SHANGGUAN Liying, et al. A consistent method without pseudo-nodes for FEM interface[J]. Chinese Journal of Computational Mechanics,2005,22(3): 374-378. (in Chinese))

[9]CHO Y S, JUN S, IM S, et al. An improved interface element with variable nodes for non-matching finite element meshes[J]. Computer Methods in Applied Mechanics and Engineering,2005,194(27/28/29): 3022-3046.

[10]王爱民, 王勖成. 有限元计算中疏密网格间过渡单元的构造[J]. 清华大学学报(自然科学版), 1999,39(8): 101-104.(WANG Aimin, WANG Xucheng. Construction of the transition elements between the sparse and dense meshes in the finite element computation[J]. Journal of Tsinghua University (Science and Technology),1999,39(8): 101-104. (in Chinese))

[11]PENG Y J, YING L P, KAMEL M M A, et al. Mesoscale fracture analysis of recycled aggregate concrete based on digital image processing technique[J]. Structural Concrete,2021,22(S1): E33-E47.

[12]JIANG X X, ZHONG H, LI D Y, et al. Three-dimensional dynamic fracture analysis using scaled boundary finite element method: a time-domain method[J]. Engineering Analysis With Boundary Elements,2022,139: 32-45.

[13]AMINPOUR M A, RANSOM J B, MCCLEARY S L. A coupled analysis method for structures with independently modelled finite element subdomains[J]. International Journal for Numerical Methods in Engineering,1995,38(21): 3695-3718.

[14]GAO Y C. A new description of the stress state at a point with applications[J]. Archive of Applied Mechanics,2003,73(3): 171-183.

[15]GAO Y C. Complementary energy principle for large elastic deformation[J]. Science in China Series G,2006,49(3): 341-356.

[16]彭一江. 基于基面力概念的新型有限元方法[D]. 北京: 北京交通大学, 2006.(PENG Yijiang. A new finite element method based on the concept of base force[D]. Beijing: Beijing Jiaotong University, 2006. (in Chinese))

[17]PENG Y J, GUO Q, ZHANG Z F, et al. Application of base force element method on complementary energy principle to rock mechanics problems[J]. Mathematical Problems in Engineering,2015,2015: 292809.

[18]PENG Y J, LIU Y H. Base force element method of complementary energy principle for large rotation problems[J]. Acta Mechanica Sinica,2009,25(4): 507-515.

[19]PENG Y J, BAI Y Q, GUO Q. Analysis of plane frame structure using base force element method[J]. Structural Engineering and Mechanics,2017,62(1): 11-20.

[20]PENG Y J, ZONG N N, ZHANG L J, et al. Application of 2D base force element method with complementary energy principle for arbitrary meshes[J]. Engineering Computations,2014,31(4): 691-708.

[21]龚琳琦, 陈曦昀, 郭庆, 等. 基面力单元法在空间几何非线性问题中的应用[J]. 应用数学和力学, 2021,〖STHZ〗42(8): 785-793.(GONG Linqi, CHEN Xiyun, GUO Qing, et al. Application of the base force element method to spacial geometrically nonlinear problems[J]. Applied Mathematics and Mechanics,2021,42(8): 785-793. (in Chinese))

[22]WANG Y, PENG Y J, KAMEL M M A, et al. Base force element method based on the complementary energy principle for the damage analysis of recycled aggregate concrete[J]. International Journal for Numerical Methods in Engineering,2020,121(7): 1484-1506.

[23]WANG Y, PENG Y J, KAMEL M M A, et al. Modeling interfacial transition zone of RAC based on a degenerate element of BFEM[J]. Construction and Building Materials,2020,252: 119063.

[24]强天驰, 寇晓东, 周维垣. 三维有限元网格加密方法及其工程应用[J]. 水利学报, 2000,〖STHZ〗31(7): 38-43.(QIANG Tianchi, KOU Xiaodong, ZHOU Weiyuan. The mesh densification method for 3D FEM and its application[J]. Journal of Hydraulic Engineering,2000,31(7): 38-43. (in Chinese))

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