摄动有限元法解一般轴对称壳几何非线性问题
Perturbation Finite Element Method for Solving Geometrically Non-linear Problems of Axisymmetrical Shell
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摘要: 本文在处理几何非线性问题时,利用在变分方程中引入振动过程,得到各级变分摄动方程,并通过有限元法求解.由于有限元法能成功地处理各种复杂边界条件、几何形状的力学问题,摄动法又可将非线性问题转化为线性问题求解.若结合这两种方法的优点,将能够解决大量复杂的非线性力学问题.并能够消除单独使用有限元法或摄动法求解复杂非线性问题所出现的困难. 本文应用摄动有限元法求解了一般轴对称壳的几何非线性问题.Abstract: In analysing the geometrically nonlinear problem of an axisymmetrical thin-walled shell,the paper combines the perturbation method with the finite element method by introducing the former into the variational equation to obtain a series of linear equations of different orders and then solving the equations with the latter. It is well-known that the finite element method can be used to deal with difficult problems as in the case of structures with complicated shapes or boundary conditions,and the perturbation method can change the nonlinear problems into linear ones. Evidently the combination of the two methods will give an efficient solution to many difficult nonlinear problems and clear away some obstacles resulted from using any of the two methods solely.The paper derives all the formulas concerning an axisym-metric. shell of large deformation by means of the perturbation finite element method and gives two numerical examples,the results of which show good convergence characteristics.
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[1] Chien Wei-zang,Large deflection of a circular clamped plate under uniform pressure,Chinese Journal of Physics,7,(2),(1947),102-113. [2] 钱伟长、林鸿荪、胡海昌、叶开沅,《弹性圆薄板大挠度问题》.中国科学院出版(1954). [3] Stanley,p.,Nonlinear Problems in Stress Analysis,Applied Science Publishers LTD,London,(1978). [4] Zienkiewicz,O.C.,The Finite Element Method,(1977). [5] 李大潜等,《有限元素法选讲》,科学出版社(1976). [6] Tottenham,H.and S.Y.Barony,Mixed finite element formulation for geometrically nonlinear analysis of shells of revolution,International Journal for Numerical Methods in Engineering,12,2,(1978),195-201. [7] 谢志成、王瑞五、杨学忠、钱振东,在材料非线性问题中的摄动有限元法,应用数学和力学.4,1(1983). -
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