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精确解析法的子结构算法
引用本文:纪振义,叶开沅.精确解析法的子结构算法[J].应用数学和力学,1990,11(10):855-860.
作者姓名:纪振义  叶开沅
作者单位:安徽建筑工业学院 (纪振义),兰州大学(叶开沅)
摘    要:文1]提出精确解析法,用以求解任意变系数常微分方程,并利用初参数算法给出一个解的解析表达式.但利用初参数算法,对某一类问题,如长柱壳弯曲和振动等,它们的解将难以在计算机上得到.本文通过非均匀轴对称长圆柱壳弯曲问题,给出精确解析法的子结构算法,它能够计算初参数算法在计算机上不能解决的问题.问题最后和初参数算法一样能归结为求解一个低阶代数方程组.文末给出算例,表明本文算法的正确性,并和初参数算法作了比较.

关 键 词:子结构算法  精确解析法  长圆柱壳

Substructure Computational Algorithm for Exact Analytic Method
Ji Zhen-yi.Substructure Computational Algorithm for Exact Analytic Method[J].Applied Mathematics and Mechanics,1990,11(10):855-860.
Authors:Ji Zhen-yi
Abstract:In 1], the exact analytic method for the solution of differential equation with variable coefficients was suggested and an analytic expression of solution was given by initial parameter algorithm. But to some problems such as the bending, free vibration and buckling of nonhomogeneous long cylinders, it is difficult to obtain their solutions by the initial parameter algorithm on computer. In this paper, the substructure computational algorithm for the exact analytic method is presented through the bending of non-homogeneous long cylindrical shell. This substructure algorithm can be applied to solve the problems which can not be calculated by the initial parameter algorithm on computer. Finally, the problems can be reduced to solving a low order system of algebraic equations like the initial parameter algorithm.Numerical examples are given and compared with the initial para-algorithm at the end of the paper, which confirms the correctness of the substructure computational algorithm.
Keywords:substructure computational algorithm  exact analytic method  long cylindrical shell
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