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Two new eight node brick element-three dimension discrete operator difference method

Tian Zhongxu1  Tang Limin2  Liu Zhengxing1  Zhang Lizhi3

(1Shanghai University, Shanghai Enhanced Laboratory of Manufacturing Automation &Robotic, 200072

2Dept. of Eng. Mechanics, Shanghai Jiaotong Univ., Shanghai 200030

3Dept. of Eng. Mechanics, Dalian Univ. Of Technology, Dalian 116024

4The company of Jilin oil field, 131100)

 

Abstract

Discrete operator difference method was given for elastic problems in three-dimension. The properties of the method in three-dimension were talked about in order to provide some basic material for its further development and some reference for the study of solutions by using weak form equations. A weak form equation containing boundary parameters was given for elastic problems in three-dimension. Both finite element method and discrete operator difference method can be pushed forward from which. Two eight-node brick elements were generated using discrete operator difference method. Although the displacements are non-conforming, their discrete schemes are convergent without additional disposal. Furthermore, this method is very simple both in formulas generating and in programming, and the computational results are stable while the meshes are changed.

 

Key words: weak forms; driving equation; discrete operator difference method; finite element method

 

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[1]    PBmwYֵӋ΢ӵxɢ(һ)()BWԺW19731ͣ3 (Tan Limin. Discrete Method for differential operators in computations for continue structures (1)&(2). 1973,(1)&(3)in chinese)

[2]    叝}һNʽxɢӽⷨӋWW200017(2)163-169 (Tian Zhongxu, Tang Limin, A Weak Form Discrete Operator Method for Solving Thin Plate Bending Problems, Chinese J of Comput. Mech., 1999, 16(1)1-7in chinese)

[3]    R˂Ζ|WʽVx̵Ľ͑BWW200141(1)1-8. (Tang Limin, Qi Zhaohui, Ding Kewei, Tian Zhongxu, He Dongsheng. Journal of Dalian University of Technology. 200141(1)1-8in chinese)

[4]    O.C.Zienkiewicz and R.L.Taylor, The Finite Element Method, (Fourth Edition), Mcgraw-Hill Book Company, 1988.

[5]    ꐽָf8-21cKwf{ԪӋWW199714(1): 43-50Chen Jianyun, Lin Gao, Chen Wanji, 8-21 Node Brick element of Refined Non-conforming Elements, Chinese J of Comput. Mech., 1997, 14(1)43-50in chinese

[6]    M.J.Loikkanen and B.M.Irons, A 8-Node Brick Finite Element, Int. J. Numer. Methods Eng., 1984, 20: 523-528

[7]    Wanji Chen and Y.K.Cheung, Three-Dimensional 8-Node and 20-Node Refined Hybrid Isoparametric Elements, Int. J. Numer. Methods Eng., 1992, 35: 1971-1889

[8]    R.L.Spilker and S.P.Singh, Three-Dimensional Hybrid-Stress Isoparametric Quadratic Displacement Elements, Int. J. Numer. Methods Eng., 1982, 18: 445-465

 


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