不均匀随机参数桁架结构的随机反应分析  

STOCHASTIC RESPONSE ANALYSIS OF TRUSS WITH INHOMOGENEOUS RANDOM PARAMETERS

作　　者：胡太彬[1] 陈建军[1] 王小兵[1] 张建国[1] 

机构地区：[1]西安电子科技大学机电工程学院,西安710071

出　　处：《工程力学》2007年第2期126-131,共6页Engineering Mechanics

基　　金：陕西省自然科学基金(2002A14);国防预研基金(51421060505DZ0155)

摘　　要：以随机荷载作用下的不均匀随机参数桁架结构为研究对象,提出了求解结构反应数字特征的矩法。从结构有限元方程出发,推导出结构刚度矩阵对各单元的弹性模量、横截面积以及各节点坐标的导数,进一步导得结构位移反应对各随机参数的敏度。利用随机变量函数的矩法,导出了结构位移反应的均值和方差,依据单元位移应力的转换表达式,分析了应力反应的均值和方差。算例表明,结构反应的方差取决于各随机参数的分散性和参数间的相关性。The moment method for stochastic truss analysis with inhomogeneous random parameters is studied. From the expression of structural stiffness matrix, its derivatives with respect to physical parameters and node coordinate are analyzed. The differential expression of structural response is educed from structural static finite element equation. Considering structural parameters and force as inhomogeneous random parameters, the mean value and the variance of structural displacement response are calculated by moment method, and the mean value and the variance of structural stress response are calculated from element physics equation. Finally, two examples are analyzed, validating the feasibility of this method. The results indicate that the randomness of response of inhomogeneous stochastic truss has relation to the randomness of different parameters and the correlation coefficient of parameters.

关 键 词：结构力学 反应分析 矩法 随机荷载 随机参数 不均匀随机场 

分 类 号：TB114[理学—概率论与数理统计] TB121[理学—数学]