利用屈曲本征方程的形式解推导出随机屈曲本征值满足的概率密度演化方程。以对数风剖面中的10 m高平均风速和地面粗糙度为随机变量,分析了超大型冷却塔的随机屈曲承载力。进而,计算出其均值及标准差。结果表明,随机屈曲承载力的概率密度函数具有一般形式,不易采用常见的概率分布模型拟合。随机屈曲承载力均值与按照均值参数计算的屈曲承载力接近,但其变异性介于两个随机变量的变异性之间。

Based on the formal solutions of the buckling eigen equation,the probability density evolution equation for the random buckling eigenvalue is derived considering the random wind loading.Taking the averaged wind speed at 10m height and roughness length as the random factors,the random buckling bearing capacity for a super-high cooling tower is then analyzed.Furthermore,both the mean and the standard deviations of the capacity are calculated.It is indicated that there exhibits a general shape for the probability density function of the random buckling capacity.And the mean of the random buckling bearing capacity is close to that one computed by the averaged parameter.However,the variation of the random buckling bearing capacity is between the corresponding values of averaged wind speed at 10m height and roughness length.

陕西省教育厅专项科研计划项目（2010JK624）