SPLITTING MODULUS FINITE ELEMENT METHOD FOR ORTHOGONAL ANISOTROPIC PLATE BENGING

Applied Mathematics and Mechanics (English Edition) ›› 2001, Vol. 22 ›› Issue (9): 1046-1056.

SPLITTING MODULUS FINITE ELEMENT METHOD FOR ORTHOGONAL ANISOTROPIC PLATE BENGING

党发宁¹, 荣廷玉², 孙训方²

1. Institute of Geotechnical Engineering, Xi’an University of Technology, Xi’an 710048, P R China;
2. Department of Applied Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, P R China

收稿日期:2000-02-28 修回日期:2001-03-23 出版日期:2001-09-18 发布日期:2001-09-18
基金资助:
China Post doctoral Science Foundation

SPLITTING MODULUS FINITE ELEMENT METHOD FOR ORTHOGONAL ANISOTROPIC PLATE BENGING

DANG Fa-ning¹, RONG Ting-yu, SUN Xun-fang²

1. Institute of Geotechnical Engineering, Xi’an University of Technology, Xi’an 710048, P R China;
2. Department of Applied Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, P R China

Received:2000-02-28 Revised:2001-03-23 Online:2001-09-18 Published:2001-09-18
Supported by:
China Post doctoral Science Foundation

摘要/Abstract

摘要： Splitting modulus variational principle in linear theory of solid mechanics was introduced, the principle for thin plate was derived, and splitting modulus finite element method of thin plate was established too. The distinctive feature of the splitting model is that its functional contains one or more arbitrary additional parameters, called splitting factors, so stiffness of the model can be adjusted by properly selecting the splitting factors. Examples show that splitting modulus method has high precision and the ability to conquer some ill-conditioned problems in usual finite elements. The cause why the new method could transform the ill-conditioned problems into well-conditioned problem, is analyzed finally.

Abstract: Splitting modulus variational principle in linear theory of solid mechanics was introduced, the principle for thin plate was derived, and splitting modulus finite element method of thin plate was established too. The distinctive feature of the splitting model is that its functional contains one or more arbitrary additional parameters, called splitting factors, so stiffness of the model can be adjusted by properly selecting the splitting factors. Examples show that splitting modulus method has high precision and the ability to conquer some ill-conditioned problems in usual finite elements. The cause why the new method could transform the ill-conditioned problems into well-conditioned problem, is analyzed finally.

中图分类号:

O242.21

党发宁;荣廷玉;孙训方. SPLITTING MODULUS FINITE ELEMENT METHOD FOR ORTHOGONAL ANISOTROPIC PLATE BENGING[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(9): 1046-1056.

DANG Fa-ning;RONG Ting-yu;SUN Xun-fang. SPLITTING MODULUS FINITE ELEMENT METHOD FOR ORTHOGONAL ANISOTROPIC PLATE BENGING[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(9): 1046-1056.

参考文献

[1] Clough R W. The finite element method in plane stress analysis[J]. Pro Amer Soc Civil Eng,1960,87:345-378.
[2] Argyris J H. Energy Theorems and Structural Analysis[M]. Butterworth,1960.
[3] Turner M J, Clough R W, Martin H G, et al. Stiffness and deflection analysis of complex structures[J]. J Aero Sci,1956,23:805-823.
[4] Fraeijs de Veubeke B. Displacement and equilibrium models in the finite element method[A]. In: Zienkiewicz O C, Holister G S Eds.Stress Analysis[C]. London: John Wiley and Sons Ltd. 1965,145-197.
[5] Pian T H H. Derivation of element stiffness matrices[J]. AIAA J,1964,2:576-577.
[6] Pian T H H. Derivation of element stiffness matrices by assumed stress distributions[J]. AIAA J,1964,2:1333-1336.
[7] Herrmann L R. A bending analysis for plates[A]. In: 1st Conf Matrix Methods in Structural Mechanics[C]. Ohio: Wright-Patterson Air Force Base,1965,577-604.
[8] Pan Y S, Chen D P. Formulation of hybrid/mixed plate bending element with splitting and partialy compatible displacements[A]. In: Proc of International Conf on Computational Engineering Mechanics[C] ,Beijing:1987,37-42.
[9] Fraeijs de Veubeke B. Upper and lower bounds in matrix structural analysis[A]. In: Fraeijs de Veubeke B Ed. Matrix Methods of Structural Analysis[C]. New York: MacMillian,1964,1:165-201.
[10] Sander P G. Bormes superieures et inferieures dans 1'analyse matricielle des plaques en flexion-torsion[J]. Bull Soc Royale Seiences Liege,1964,33(7):456-494.
[11] RONG Ting-yu.A variational principle with split modulus in elasticity[J].Journal of Southwest Jiaotong University,1981,1:48-55.(in Chinese).
[12] RONG Ting-yu. Generalized mixed variational principles and new FEM models in solid mechanics[J]. Int J Solid Structures,1988,24(1):1131-1140.
[13] Zienkiwicz O C. The Finite Element Method in Engineering Science[M]. McGraw-Hill Book Company,1971.
[14] Leknitskii S G. Anisotropic Plates[M]. London: Gordon & Breach,1968.
[15] Timoshenko S, Woinowsky-Kreger S. Theory of Plates & Shells[M]. New York: McGraw-Hill Book Company,1959.
[16] Herrmann L R.Finite element bending analysis for plates[J].J En gn Mech 1967.
[17] DANG Fa-ning Method of generalized mixed finite elements and its application to the research on ill-conditioned problems[D].Ph D Thesis.Chengdu:Southwest Jiaotong University,1998,1:54-74.(in Chinese).

SPLITTING MODULUS FINITE ELEMENT METHOD FOR ORTHOGONAL ANISOTROPIC PLATE BENGING

SPLITTING MODULUS FINITE ELEMENT METHOD FOR ORTHOGONAL ANISOTROPIC PLATE BENGING

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