结构边界条件随机性的加权残值处理方法

Method of Weighted Residuals for Dealing with Randomness of Boundary Conditions in Structures

基于随机结构的加权残值方法提出了一种处理结构边界条件随机性的方法,基本作法是在边界条件中引入一个零均值的随机变量,利用加权残值法得到待求问题解,包括此随机变量的近似函数表达式,再应用求解随机变量函数的矩法便可得到所求问题的一、二阶矩等数字特征,并可方便地得到边界条件分散性对结果分散性的影响程度,实现了对结构边界条件随机性的分析。通过两算例的结果与Monte-Carlo模拟法结果相比较,证明了方法的正确性和便捷性,并得到了一些重要的结论。

Based on the method of weighted residuals for stochastic structures, the paper presents a new analysis method for randomness of boundary conditions in structures. A stochastic variable with a zeromean value is introduced in boundary conditions. An approximate function expression of a problem to be solved can be deduced by the weighted residual method, and then the first and second moment of a random function can be calculated with a method of moment. Thus randomness of boundary conditions is analysed, and the effect on structural reaction from randomness of boundary conditions is obtained expediently. At the end of the paper the present method is illustrated by two examples. Comparison with the results of Monte-Carlo method shows that the method is correct. Some valuable conclusions are obtained.