Four-node Plane Element Model on Complementary Energy Based on the Concept of Base Line Forces

PENG Yi-jiang; LEI Wen-xian; PENG Hong-tao

Journal of Beijing University of Technology > 2009 > 35(11): 1484-1490.

PENG Yi-jiang, LEI Wen-xian, PENG Hong-tao. Four-node Plane Element Model on Complementary Energy Based on the Concept of Base Line Forces[J]. Journal of Beijing University of Technology, 2009, 35(11): 1484-1490.

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Four-node Plane Element Model on Complementary Energy Based on the Concept of Base Line Forces

1. Key Lab of Urban Security & Disaster Engineering, Beijing University of Technology, Beijing 100124, China;
2. Department of Engineering Mechanics, Institute of Astronautics & Aeronautics, Tsinghua University, Beijing 100084, China;
3. College of Water Conservancy and Civil Engineering, China Agricultural University, Beijing 100083, China;
4. Institute for Soil and Water Conservation, Chinese Academy of Sciences, Yangling 712100, Shaanxi, China

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Received Date: February 27, 2008
Available Online: December 09, 2022

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Abstract

Using the base line forces as fundamental variables to describe the stress state for two dimension problems and the displacement gradients that are the conjugate variables of the base line forces,which describe the deformation state of objects,a 4-node plane element model based on complementary energy principle is proposed.In this paper,the complementary energy of an element is constructed by using the base line forces.The equilibrium conditions are released by the Lagrange multiplier method,and a modified complementary energy principle described by the base line forces is obtained.The formulation of the 4-node plane element is derived by assuming that the stress is uniformly distributed on each face of a plane element.A finite element procedure of complementary energy principle is developed using MATLAB language.The numerical results of examples show that this model has high precision and is free from mesh sensitivity.
- complementary energy principle,
- finite element,
- compliance matrix,
- 4-node plane element,
- Lagrange multiplier method,
- base forces,
- base line forces

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[1]	ZIENKIEWICZ O C.The finite element method[M].New York:McGraw-Hill,1977.
[2]	COOK R D.Concepts and applications of finite element analysis[M].New York:Wiley,1981.
[3]	BATHE K J.Finite element procedures[M].New Jersey:Prentice-Hall,1996.
[4]	王金彦,陈军,李明辉.非线性有限元分析的非协调模式及存在的问题[J].力学进展,2004,34(4):455-462.WANG Jin-yan,CHEN Jun,LI Ming-hui.The state-of-the-art of incompatible mode of non-linear FEM and the issues[J].Advances in Mechanics,2004,34(4):455-462.(in Chinese)
[5]	GAO Y C.A new description of the stress state at a point with applications[J].Archive Appl Mech,2003,73(3/4):171-183.
[6]	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)
[7]	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 finite element method on potential energy principle by base forces[J].Journal of BeijingUniversity of Technology,2007,33(7):687-692.(in Chinese)
[8]	彭一江,金明.基于基面力概念的一种新型余能原理有限元方法[J].应用力学学报,2006,23(4):649-652.PENG Yi-jiang,JIN Ming.New complementary finite-element method based on base forces[J].Chinese Journal of AppliedMechanics,2006,23(4):649-652.(in Chinese)
[9]	彭一江,金明.基于基面力概念的余能原理任意网格有限元方法[J].工程力学学报,2007,24(10):41-45.PENG Yi-jiang,JIN Ming.Finite element method for arbitrary meshes based on complementary energy principle using baseforces[J].Engineering Mechanics,2007,24(10):41-45.(in Chinese)
[10]	彭一江,刘应华.一种基于基线力概念的平面几何非线性余能原理有限元模型[J].固体力学学报,2008,29(4):365-371.PENG Yi-jiang,LIU Ying-hua.A finite element model of complementary energy principle for geometrically nonlinear planeproblem based on the concept of base line forces[J].Acta Mechanica Solida Sinica,2008,29(4):365-371.(in Chinese)
[11]	彭一江,刘应华.基面力概念在几何非线性余能有限元中的应用[J].力学学报,2008,40(4):496-501.PENG Yi-jiang,LIU Ying-hua.Application of the base forces concept in geometrically nonlinear finite element method oncomplementary energy[J].Acta Mechanica Sinica,2008,40(4):496-501.(in Chinese)
[12]	PENG Y J,LIU Y H.Base force element method of complementary energy principle for large rotation problems[J].ActaMechanica Sinica,2009,25(4):507-515.
[13]	高玉臣.固体力学基础[M].北京:中国铁道出版社,1999.
[14]	KIM K D,LIU G Z,HAN S C.A resultant 8-node solid-shell element for geometrically nonlinear analysis[J].CompMech,2005,35:315-331.

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