圆孔无限大板边界受力弯曲的挠度解析公式

应用弹性力学的复变函数理论，首先导出了圆孔无限大板弯曲挠度的复Fourier级数表达式，再把孔的边界条件进行复Fourier级数展开，用待定系数法确定级数的未知系数，利用复Fourier级数的卷积及广义函数论，推导出圆孔无限大板在边界弯曲时对应于常见3种孔边界条件的挠度解析公式．对孔边固支、简支、自由的圆孔无限大板的弯曲问题可直接套用求解。

The Analytical Formulas of Bending Deflection for Infinite Plates with a Unit Circle under the Boundary Loads

On the basis of the mathematical elastic theory, the bending deflection expression of the complex Fourier Series is derived at first for the infinite plate with a unit circle. Then the boundary conditions are expanded in Fourier Series on the unit circle and the unknown coefficients of the series are determined by comparing coefficients method. By means of the convolution of the complex Fourier Series and the generalized functions, the deflection analytical formulas are produced for the infinite plates with a unit circle under the boundary loads and the three common conditions at the unit circle edge. These formulas are used directly to solve the bending problems of the infinite plates with a unit circle of the clapped edge, simply supported edge or free edge.