不均匀随机参数桁架结构的随机反应分析
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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.
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.
引文
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[9]雒卫廷,陈建军,高伟.随机结构分析的加权残值方法[J].机械科学与技术.2004,23(3):147~150.Luo Weiting,Chen Jianjun,Gao Wei.Analysis of stochastic structures by method of weighted residuals[J].Mechanical Science and Technology,2004,23(3):147~150.(in Chinese)
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[2]刘宁,吕泰仁.随机有限元及其工程应用[J].力学进展.1995,25(1):114~116.Liu Ning,Lu Tairen.Stochastic FEM its applications in engineering[J].Advances in Mechanics,1995,25(1):114~116.(in Chinese)
[3]Ramu S A,Ganesan R.Response and stability of a stochastic beam-column using stochastic FEM[J].Computers and Structures.1995,54(2):207~221.
[4]Arqyris John,Papadrakakis Manolis,Stefanou Georqe.Stochastic finite element analysis of shells[J].Computer Methods in Applied Mechanics and Engineering,2002,191(41/42):4781~4804.
[5]Noh Hyuk Chun.A formulation for stochastic finite element analysis of plate structures with uncertain Poisson's ratio[J].Computer Methods in Applied Mechanics and Engineering,2004,193(45?47):4857~4873.
[6]李杰.随机结构分析的扩阶系统方法(1)扩阶系统方程[J].地震工程与工程震动,1995,15(3):111~118.Li Jie.Expanded order system method of stochastic structures analysis,Part I:equation of expanded ordersystem[J].Earthquake Engineering and Engineering Vibration,1995,15(3):111~118.(in Chinese)
[7]Chen J J,Che J W,Sun H A,Ma H B,Cui M T.Probabilistic dynamic analysis of truss structure[J].Structural Engineering and Mechanics,2002,13(2):233~239.
[8]马洪波,陈建军,崔明涛.随机参数桁架结构的有限元与可靠性分析[J].西安电子科技大学学报,2003,30(1):103~107.Ma Hongbo,Chen Jianjun,Cui Mingtao.Analysis of the finite element and reliability for stochastic truss structures[J].Journal of Xidian University,2003,30(1):103~107.(in Chinese)
[9]雒卫廷,陈建军,高伟.随机结构分析的加权残值方法[J].机械科学与技术.2004,23(3):147~150.Luo Weiting,Chen Jianjun,Gao Wei.Analysis of stochastic structures by method of weighted residuals[J].Mechanical Science and Technology,2004,23(3):147~150.(in Chinese)
[10]Zhu W Q,Ren Y J,Wu W Q.Stochastic FEM based on local averages of random vector fields[J].Journal of Engineering Mechanics,1992,118(3):496~511.
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