基于单源模糊数的模糊随机动态有限元方程的解法

A Solution for Fuzzy-stochastic Dynamic Finite Element Method by the Monosource Fuzzy Number Operations

本文提出一种模糊随机动态有限元方程的解法,指出利用单源模糊数和它的运算法则,可以把一个不含阻尼项的模糊随机动态有限元平衡方程转化为两类不同集合下的方程组,一种是模糊数方程,另一种是普通的动态有限元平衡方程。前者可用模糊数运算法则求解。通常这类方程的表达式非常简单,故很容易求解,后者可利用现有的求解随机动态随机有限元平衡方程的方法计算,这时求解该方程的计算量几乎等同于求解相应的普通随机动态有限元平衡方程的计算量。最后的算例表明,本文提出的方法与通常所用的λ截集法计算结果基本相同,而且所用的计算量远远小于用λ截集法所用的计算量。

In the paper, a method for the fuzzy-stochastic dynamic finite element is presented. By the monosource fuzzy numbers and their operations, without considering the damping factors, the fuzzy (fuzzy-stochastic) dynamic finite element equilibrium equations can be divided into two kinds of equations, one is fuzzy number equations and another is general (stochastic) dynamic finite element equilibrium equations. The first can be solved by the rules of the fuzzy number and the later can be solved by the programs in the dynamic stochastic finite element method. So the computing quantity of this solution is almost equal to that the general (stochastic) dynamic finite element method. Finally the example shows that the method presented in the paper is much simpler than the A cutting method.