The 2D Base Force Element Method Based on the Potential Energy Principle

SHAN Yan-yan; REN Cong; HUANG Si-bai; BAI Ya-qiong

doi:10.3879/j.issn.1000-0887.2016.06.008

Volume 37 Issue 6

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2016 > 37(6): 626-632

SHAN Yan-yan, REN Cong, HUANG Si-bai, BAI Ya-qiong. The 2D Base Force Element Method Based on the Potential Energy Principle[J]. Applied Mathematics and Mechanics, 2016, 37(6): 626-632. doi: 10.3879/j.issn.1000-0887.2016.06.008

Citation:

PDF( 450 KB)

The 2D Base Force Element Method Based on the Potential Energy Principle

doi: 10.3879/j.issn.1000-0887.2016.06.008

College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100124, P.R.China

Funds: The National Natural Science Foundation of China（10972025）

Received Date: 2015-12-14
Rev Recd Date: 2016-01-25
Publish Date: 2016-06-15

Abstract

Abstract

Based on the base force concept proposed by Gao Y C, the quadrangular element model of the base force element method (BFEM) for 2D linear elastic problems was proposed. Several typical examples of numerical calculation were given in view of the effect of the element’s length-to-width ratio. The BFEM results were compared with the analytic solution and the conventional triangular finite element solution as well as the isoperimetric quadrangular element (Q4 model) solution; in turn the correctness and the computing performance of the BFEM based on the potential energy principle were verified. It is shown that the BFEM gives results in good agreement with the analytic solution and has higher accuracy than the conventional finite element methods, but is not sensitive to the element’s length-to-width ratio. So the BFEM is expected to have wide application prospects.
- base force,
- potential energy principle,
- stiffness matrix

FullText(HTML)

References(15)

References

[1]	王勖成. 有限单元法[M]. 北京: 清华大学出版社, 2003: 103-121.（WANG Xu-cheng. Finite Element Method [M]. Beijing: Tsinghua University Press, 2003: 103-121.(in Chinese)）
[2]	王勖成, 邵敏. 有限单元法基本原理和数值方法[M]. 第2版. 北京: 清华大学出版社, 1997: 88-95.(WANG Xu-cheng, SHAO Min. Basic Principles of Finite Element Method and Numerical Method [M]. 2nd ed. Beijing: Tsinghua University Press, 1997: 88-95.(in Chinese))
[3]	Baudouin F de V. Displacement and equilibrium models in the finite element method[C]//Zienkiewicz O C, Holister G S, ed. Stress Analysis.New York: John Wiley & Sons, 1965: 145-197.
[4]	Wilson E L, Taylor R L, Doherty W P, Ghahoussi J. Incompatible displacement models[C]// Numerical and Computer Methods in Structural Mechanics.Academic Press, 1973: 43-57.
[5]	卞学鐄. 杂交应力有限元法的研究进展[J]. 力学进展, 2001,31(3): 344-349.(BIAN Xue-huang. The research progress of hybrid stress finite element method[J]. Mechanical Progress,2001,31(3): 344-349.(in Chinese))
[6]	Herrmann L R. A bending analysis for plates[C]//1st Conf, Matrix Methods in Structural Mechanics.Wright-Patterson Air Force Base, Ohio, 1965: 577-604.
[7]	Belytchko T, Krongauz Y, Organ D, Fleming M, Krysl P. Meshless method: an overview and recent developments[J].Computer Methods in Applied Mechanics & Engineering,1996,139(S1/S4): 47-93.
[8]	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.
[9]	Gao Y C, Gao T J. Large deformation contact of a rubber notch with a rigid wedge[J].International Journal of Solids & Structures,2000,37(32): 4319-4334.
[10]	彭一江. 基于基面力概念的新型有限元方法[D]. 博士学位论文. 北京: 北京交通大学, 2006: 31-42.（PENG Yi-jiang. A new finite element method based on the base forces[D]. PhD Thesis. Beijing: Beijing Jiaotong University, 2006: 31-42.(in Chinese)）
[11]	彭一江, 金明. 基面力的概念在势能原理有限元中的应用[J]. 北京交通大学学报, 2007,31(4): 1-4.（PENG Yi-jiang, JIN Ming. Application of the base forces concept in finite element method on potential energy principle[J]. Journal of Beijing Jiaotong University,2007, 31(4): 1-4.(in Chinese)）
[12]	彭一江, 金明. 基于基面力概念的一种新型势能原理有限元方法[J]. 北京工业大学学报, 2007,33(7): 687-692.(PENG Yi-jiang, JIN Ming. A new type of the potential energy principle of finite element method based on the concept of the base force[J]. Journal of Beijing University of Technology,2007,33(7): 687-692.(in Chinese))
[13]	PENG Yi-jiang, DONG Zhan-long, PENG Bo, LIU Ying-hua. Base force element method (BFEM) on potential energy principle for elasticity problems[J]. International Journal of Mechanics and Materials in Design,2011,7(7): 245-251.
[14]	高玉臣. 固体力学基础[M]. 北京: 中国铁道出版社, 1999: 4-7.(GAO Yu-chen. Solid Mechanics Basis[M]. Beijing: China Railway Press, 1999: 4-7.(in Chinese))
[15]	金明. 非线性连续介质力学[M]. 北京: 清华大学出版社, 北京交通大学出版社, 2005.(JIN Ming. Nonlinear Continuum Mechanics [M]. Beijing: Tsinghua University Press, Beijing Jiaotong University Press, 2005.(in Chinese))