Zhu Ju-fen, Zhou Cheng-fang, Lü He-xiang. The Nonlinear Numerical Analysis Method for Frames[J]. Applied Mathematics and Mechanics, 1987, 8(12): 1099-1109.
 Citation: Zhu Ju-fen, Zhou Cheng-fang, Lü He-xiang. The Nonlinear Numerical Analysis Method for Frames[J]. Applied Mathematics and Mechanics, 1987, 8(12): 1099-1109.

# The Nonlinear Numerical Analysis Method for Frames

• Publish Date: 1987-12-15
• This paper gives the direct formulas of stiffness matrixes of two-kinds of Kirchhoff nonlinear elements under total-Lagrange coordinate. For the first one, it includes not only the quadric terms of increments of strain and displacement but also-the influence of rotations. For the second one, it is simplified and its nonlinear is considered by taking into account the influence of axial force on the equilibrium equation in the linear beam theory.The nonlinear equation obtained from both of the above-Said elements is solved by mixed Newton-Raphson method, and by comparing the results obtained from two kinds of nonlinear beam some important conclusions that we can know how to use them right are given in our paper.
•  [1] Kamat,M.P.and L.T.Watson,A quasi-Newton versus a homotopy method for nonlinear structure analysis,Comput.and Struct.,4 (1983),579-589. [2] Suran,Karan S.,Geometrically nonlinear formulation for two dimensional curved beam elements,Comput.and Struct.,4 (1983),105-114. [3] Schrefler,B.A.and S.Odorizz,A total Lagrangian geometrically nonlinear analysis of combined beam and cable structures,Comput.and Struct.,1 (1983),115-127. [4] Fum,Fumio.A simple mixed formulation for elastic problems,Comput.and Struct.,1 (1983),79-88. [5] Stanley,P.,Nonlinear Problems in Stress Analysis (1978),373-396,. [6] 谢贻权、何福保,《弹性和塑性力学中的有限元方法》,机械工业出版社(1981). [7] Zienkiewicz,O.C.,The Finite Element Method 3rd Edn.,McGraw-Hill London (1977). [8] Majid,K.I.,Nonlinear Structures,London-Butterworths (1972). [9] Frish-Fay,R.,Flexible Bars,London-Butterworths (1962).

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