机械结构随机响应统计矩的计算方法

Computation Method of Statistical Moments of Random Response for Mechanical Structures

提出了一种计算具有不确定参数(随机载荷、材料、几何尺寸)的机械结构随机响应统计矩的实用方法.采用Chebyshev多项式节点划分基本随机变量水平,开展实验设计.利用Chebyshev多项式拟合机械结构随机响应与基本随机变量的函数关系,使用降维积分技术求解机械结构随机响应的概率统计矩.数字算例表明所提方法具有较高的计算效率和求解精度,通用性强,可以用于复杂机械结构随机响应的概率分析中.

To compute the statistical moments of the random response for mechanical structures subject to loads, material and geometry, a method was proposed. The basic random variables were discretized by the Chebyshev nodes to obtain discrete experimental samples. Then the Chebyshev approximation theory was applied to approximate the relationship of the random response-variables. The statistical moments of the random response were computed with the dimension-reduction method for multi-dimensional integration. Finally, a practical engineering case was used to demonstrate the generality and effectiveness of the proposed method.