基于广义变分原理的矩形薄板单元

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A Rectangular Element of Thin Plates Based upon the Generalized Variational Principles

1.
Shanghai University of Technology, Shanghai;
2.
Shanghai Institute of Railway Technology; Shanghai Institute of Appl. Math, and Mech., Shanghai

摘要: 本文应用广义变分原理,构造了适合正交各向异性薄板静动力分析的矩形单元MR—12.计算结果表明,基于广义变分原理的非协调元具有很好的收敛性和计算精度.证明了广义变分原理在建立非协调单元中的有效性和优越性.MR—12单元的计算格式和普通矩形板元无原则性的差别,极易推广使用.

Abstract: Based on generalized variational principles, an element called MR-12 was constructed for the static and dynamic analysis of thin plates with orthogonal anisotropy. Numerical results showed that this incompatible element converges very rapidly and has good accuracy. It was demonstrated that generalized varialional principles arc useful and effective in founding incompatible clement.Moreover, element MR-12 is easy for implementation since it does not differ very much from the common rectangular element R-12 of thin plate.

[1]	钱伟长.《广义变分原理》.知识出版社(1985).
[2]	Chien Wei-zang,Incompatible plate elements based upon generalized varitional principles,Hybrid and Mixed Finite Element Method,eds.A.N.Atluri,R.H.Gallagher and O.C.Zienkienwiez(1983),381-404.
[3]	谢贻权、何福保,《弹性和塑性力学中的有限单元法》.机械工业出版社(1981).