Xie Zhi-cheng, Wang Rei-wu, Yang Xue-zhong, Chien Zhen-dong. The Perturbation Finite Element Method for Solving Problems with Nonlinear Materials[J]. Applied Mathematics and Mechanics, 1983, 4(1): 123-134.
 Citation: Xie Zhi-cheng, Wang Rei-wu, Yang Xue-zhong, Chien Zhen-dong. The Perturbation Finite Element Method for Solving Problems with Nonlinear Materials[J]. Applied Mathematics and Mechanics, 1983, 4(1): 123-134.

# The Perturbation Finite Element Method for Solving Problems with Nonlinear Materials

• Publish Date: 1983-02-15
• The perturbation method is one of the effective methods for solving problems in nonlinear continuum mechanics. It has been developed on the basis of the linear analytical solutions for the o-riginal problems. If a simple analytical solution cannot be obtained,we would encounter difficulties in applying this method to solving certain complicated nonlinear problems. The finite element method appears to be in its turn a very useful means for solving nonlinear problems,but generally it takes too much time in computation. In. the present paper a mixed approach,namely,the perturbation finite element method,is introduced,which incorporates the advantages of the two above-mentioned methods and enables us to solve more complicated nonlinear problems with great saving in computing time.Problems in the elastoplastic region have been discussed and a numerical solution for a plate with a central hole under tension is given in this paper.
•  [1] Thomson,J.M.T.and A.C.Walker,The nonlinear perturbation analysis of discrete structural systems,International Journal of Solids and Structures,4,8,(1966). [2] Gallagher, R.H,非线性有限元结构分析中的摄动法,有限元素法及其在力学中的应用,译文集.译自Computational Mechanics, (1974) [3] Yokoo,Y.,T.Nakamura and K.Uetani,The incremental perturbation method for large displacement analysis of elastic-plastic structures,Int.J.Numerical Methods in Engineering,Vol.10,No.3,(1976). [4] Trifan,D.,On the plastic bending of circular plates,Quart,of Applied Mathematics,16,(1948). [5] 古国纪,顾求林,弹塑性圆板大挠度问题,力学学报,2,3,(1958). [6] 顾求林,有强化弹塑性平面问题的一段渐近解,清华大学基础部科研报告(未发表),(1980). [7] 李大潜等,《有限元素法续讲》,科学出版社. [8] 周春田,带有缺陷板在单向拉伸时弹性应力应变场的测定,清华大学基础部科研报告(未发表),(1981). [9] 钱伟长,《变分法及有限元》,科学出版社,(1980). [10] 钱伟长.林鸿荪.胡海昌.叶开沅.《弹性圆薄板大挠度问题》,中国科学院.(1954). [11] Washizu,K.,Variational Methods in Elasticity and Plasticity,(1968). [12] Zienkiewicz,O.C.,The Finite Element Method,(1977).

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