旋转变厚度圆盘的样条积分方程法

A SPLINE INTEGRAL EQUATION METHOD FOR ROTATING VARIABLE-THICKNESS DISC

一、前言 对于旋转变厚度圆盘的应力分析,一般可用有限元法或差分法,但相对于边界元来说精度较差,若要提高精度就必须将单元分细,随之而来的是方程阶数的增加和计算时间的增长。为了克服上述缺点,本文提出了一种新的样条积分方程法,直接利用弹性力学二维问题的环基本解建立积分方程并用样条函数进行求解。这样只需划分少量单元,就可获得精度很高的数值解,可大大节约计算机内存和计算时间。

The integral equations of rotating disc with variable thickness are derived by means of the ring fundamental solution of elacticity. Then the integral equations are solved by spline function method. Also, this method is applied to the rotating variable-thickness disc with circular hole. Its computing program is so simple as to work on the IBM-PC computer. Due to the spline interpolation, very high accuracy of the numerical solution can be achieved even if few elements are chosen, The numerical results obtained by this method is almost completely consistent with the exact solution . Obviously , this method overcomes the shortcomings of the finite element method or finte difference method in need of solving huge systems of algebraical equations.