有限长圆柱体轴对称问题的弹性理论解

本文利用H变换和Stockes变换.导出双变量函数及其编导数在闭区间上完整的双级数表达式,从而求得弹性力学中有限长圆柱体的轴对称问题的一般解析解.文中以轴向拉伸圆柱体为例,考虑不同的外力作用区域,分析了圆柱体上位移和应力的分布.本文所提的方法具有一般性.可以用来求解其它学科领域中有关柱坐标的轴对称边值问题.

An Elasticity Solution for Axisymmetric Problem of Finite Circular Cylinder

In this paper, the complete double-series in the closed region expressing the double-variable functions and their partial derivatives are derived by the H-trans-formation and Stockes' transformation. Using the double-series, a series solution for the axisymmetric boundary value problem of the elastic circular cylinder with finite length is presented. In a numerical example, the cylinder subjected to the axisymmetric tractions with various loaded regions is investigated and the distributions of the displacements and stresses are obtained. It is possible to solve the axisymmetric boundary value problems in the cylindrical coordinates for other scientific fields by use of the method presented in this paper.