具空间随机刚度薄圆板的轴对称弯曲精确解

Exact solution of the bending of circular plate with spatially stochastic stiffness

研究了具空间随机刚度的薄圆板的轴对称弯曲精确解 .假设空间随机刚度的概率分布已知 ,基于确定性的薄圆板的控制方程和边界条件 ,推导了随机薄圆板挠度的精度的均值和协方差函数 .这种精确解对于检验其他近似分析方法的准确性是很有意义的 .

The exact solution of the axisymmetric bending of the circular plate with spatially varying stochastic stiffness is presented. The method solving the problem is a new one being different from perturbation or series expansion methods. Assuming the probabilistic density of the random variation is known, the exact mean and variance functions of the displacement is derived using control equation and boundary conditions of the deterministic plate. In the other hand, this paper compares the exact solution with perturbation result of the center of the plate. It is shown that the exact solution is useful for checking the accuracy of various approximate methods.