随机有限元方程一般式的两种推导方法

８０年代初发展起来的随限元法是解决随机问题强有力的数值分析工具，如随机动力学、随机场及结构强度的可靠性等等问题，本文从有限元基本方程出发，分别采用对有限元方程按Ｔａｙｌｏｒ级数展开和对有限元方程求偏导数等方法。推导了随机有限元基本方程的一般式，并用数学归纳法证明了上述两种方法推导结果的与等效性，本文研究表明，Ｔａｙｌｏｒ级数展开法推导，数学意义明确，但推导过程较为复杂；而按求偏导数法，数学意义不够

Two Methods for Deriving General Formulas of Stochastic Finite Element Methods

The stochastic finite element method (SFEM) developed in the beginning of 1980's is a powerful tool of the numerical analysis for solving random problems, such as stochastic dynamics, stochastic fields and the reliability of structure strength and so on. From the fundamental equations of finite element methods?general formulas of SFEM are respectively derived with Taylor' s expansion series to finite element formulas and partial differentiation with respect to finite element formulas in this paper, and the correctness and equivalence of the above results are proved by the mathematical induction method. The investigation shows that the results obtained by Taylor' s expansion are clear in mathematical concepts but complicated in the processes of derivation, and the results obtained by partial differentiation are simple in the processes of derivation but unclear in mathematical concepts. For calculating the means and the variance of objective random variables, the accuracy of the numerical results is the same in the amount class if the fun damental formulas of stochastic finite element methods are established by the above two methods.