刘腾喜, 王磊. 样条有限点法分析板的大挠度问题[J]. 工程力学, 1987, 4(3): 19-28.
引用本文: 刘腾喜, 王磊. 样条有限点法分析板的大挠度问题[J]. 工程力学, 1987, 4(3): 19-28.
Liu Tengxi, Wang Lei. SPLINE FINITE POINT METHOD FOR THE GEOMETRICALLY NONLINEAR ANALYSIS OF PLATES[J]. Engineering Mechanics, 1987, 4(3): 19-28.
Citation: Liu Tengxi, Wang Lei. SPLINE FINITE POINT METHOD FOR THE GEOMETRICALLY NONLINEAR ANALYSIS OF PLATES[J]. Engineering Mechanics, 1987, 4(3): 19-28.

样条有限点法分析板的大挠度问题

SPLINE FINITE POINT METHOD FOR THE GEOMETRICALLY NONLINEAR ANALYSIS OF PLATES

  • 摘要: 样条有限点法已成功地应用于板的线性分析。本文用样条有限点法求解几何非线性平板,以位移u、u和W作为基本未知量,采用三次B样条插值函数与梁函数级数的乘积作为位移试函数,从最小势能原理出发建立基本方程,推导了非线性切线刚度矩阵,用改进的Newton-Raphson方法求解非线性方程组,最后给出了算例,其结果与一些已有的成果进行了比较,表明该方法分析板壳结构的非线性问题是十分有效的。

     

    Abstract: The spline finite point method has been used successfully in the linear analysis of plates. In this thesis, it is presented for the geometrically nonlinear analysis of plates. The displacement components u. v and ware treated as fundamental variables, taking the form of a product of the cubic spline interpolating functions and series. The essential equations are estadlished through the principle of minimum potential energy. The expresion of the tangential stiffness matrix in the spline finite point method is obtained. The system of nonlinear equations is solved by means of the modified Newton-Raphson method. Some computational examples are given in the end of paper. The deflections and moments of the simple supported rectangular plates and the clamped square plates under the uniform load or the central concentrated load are calculated. The results obtained is compared with those reported. Because of the using of spline function the results have high accuracy and the method can be easily carried out with computer. In comparison with the finite element method, the spline finite point method has the following advantages: fewer variables and input data of the program, shorter CPU time, The results show that this method is effective for the geometrically nonlinear analysis of the plate and shell structures.

     

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