有限元广义应力影响函数定理及算法

The Theorem for the Analysis of Influence Functions of the Generalized Stress and Its Algorithm

当一个定向的单位集中力在结构上移动时,结构某处某应力分量的值是该力位置的函数,称为应力影响函数.本文作者曾经提出并证明了连续体和有限元模型的平均应力影响函数定理,设计了算法,编制了程序,可用于求各类单元组成的复杂结构的应力影响函数,并已应用于工程中。本文发展上述理论,提出有限元模型广义应力影响函数定理,据此可用间接法一次求得任意单元中任一点应力分量或由应力分量的线性组合表示的物理量的影响函数。讨论了单元基准节点位移模式的单元特征向量求法。

The internal force influence functions of trusses, frames and grids can be analyzed by the use of indirect method on the basis of the Muller-Breslau's principle [1, 2]. In references [3, 4, 5] the author has developed a similar theorem for the finite element model. Using it the influence functions of the average stress of an element can be calculated efficiently.For higher-order elements the stress field of an element is complicated. It cannot be represented by its average value. In this paper the concept of the generalized stress of an element is introduced and the theorem for the analysis of influence function of the generalized stress is proposed and proved. Based on it the influence function of stress at any position of an element can be analyzed efficiently by the use of indirect method. The algorithm is discussed in detail.