一种非线性问题的随机载荷近似解法

在增量非线性有限元法的基础上，引用摄动技术将随机载荷分为确定性部分和摄动随机部分，把确定性部分看做摄动部分的线性基础，提出了在线性随机有限元基础上的小摄动非线性随机载荷近似解方法。这种方法可应用于现有的增量非线性有限元法，具有程序设计简单，有效利用非线性有限元分析程序等优点。

An Approximate Solution of Nonlinear Structure under Random Loading

In recent years, the studies in the field of nonlinear stochastic finite element analysis introduce the perturbation technique to deal with the stochastic factors in the problem. The existing methods generally involve taking partial differential of stiffness matrix to the factors, and therefore, they are usually fussy and difficult to be realized in engineering. This paper presents an approximate method to deal with the random loads applied to nonlinear structures, in which the random loads are separated into two parts: one is determinate and the other is perturbational. Based upon the solutions of the conventional nonlinear finite element method(FEM), this method is used to solve the material-nonlinear problems without additional partial differential of stiffness matrix. The numerical example presented in this paper shows that the method, when using the existing program of nonlinear finite element analysis, has some advantages such as simple programming and higher efficiency than the existing methods.