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A Simple Spline Integral Equation Method for Circular Plates with Variable Thickness

机译：变厚圆板的简单样条积分方程法

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摘要

A simple spline integral equation method is presented in this paper for the axisymmetrical bending of circular plates with variable thickness. Firstly, the fundamental solution of a second-order differential equation is derived. With the slope of the deflection surface taken as an unknown function, an integral equation is then established for circular plates with variable thickness. The integral equation is solved numerically by cubic spline interpolation and the deflection and bending moment at any point within the circular plate are obtained. Finally, the validity of the proposed method is verified with the analytical solution obtained from the literature.
机译：提出了一种简单的样条积分方程方法，用于变厚度圆板的轴对称弯曲。首先，推导了二阶微分方程的基本解。将偏转表面的斜率作为未知函数，然后针对厚度可变的圆形板建立积分方程。通过三次样条插值法对积分方程进行数值求解，并获得了圆盘内任意点的挠曲和弯矩。最后，从文献中获得的解析解验证了该方法的有效性。

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