确定一类弹性力学方程通解的简便方法

Simple Method of Determining General Solution of Elasticity Equation

在弹性力学问题的极坐标解答中,经常会遇到一类可转化为欧拉方程的常微分方程。在现有的教材中,均采用先将此类方程转化为欧拉方程,然后再求解的讲授思路,但由于转化过程过于繁杂,以至学生在学习此部分内容时普遍感到困难。利用幂函数做试探解,可非常简便地确定此类方程的特征根,并由此确定出方程的通解。作者多年的教学实践证明了该方法的有效性。

A kind of ordinary difference equation that can be transferred to Euler equation, often appears in polar coordinates solution of elastic problems. In current course, firstly, this kind of equation is transformed to Euler equation, then the method of solution is presented. But the process of transformation is too cockamamie, so the students feel it difficulty while learning. Utilizing power function as trial solution, the eigenvalue of this equation is simply and conveniently determined, and the general solution is obtained. The teaching practice of the author had showed the availability of this method.