随机结构孤立特征值的统计特性

Statistics of Isolated Eigenvalues of Random Structures

研究了随机结构的孤立特征值问题。将材料物理量的随机场扩展为K L(Karhunen Loeve)正交展式,采用非正交多项式混沌展式表达孤立特征值,建立了和摄动法类似的一系列确定的递推方程,并通过确定性有限元方法求解了这些递推方程,得到了特征值的均值和方差。在算例中用蒙特卡洛方法验证了本方法的正确性。

A new random finite element method for solving eigenvalue problems involving material variability is given, The random material properties, such as the modulus of elasticity, are represented by Karhunun-Loeve expansion. Random structural eigenvalues are expressed as nonorthogonal polynomials chaos. With the aid of the finite element method, a set of deterministic recursive equations is set up to deal with eigenvalue problems through nonorthogonal polynomials of the same order. The statistics of eigenvalues is derived. A beam problem and a plate problem are investigated by the new method. The derived second order statistics of eigenvalues is found in good agreement with those obtained by Monte-Carlo simulation.