结构内力概率密度演化的向量马氏过程方法

本文提出了位移加载机制下求解无启发持性结构结点力的概率密度演化规律的方法。该方法将力与非线性构形状态演化联合起来。组成力-状态混合向量马氏过程。采用分离式分析方法进行状态转移概率速度分析。然后建立力-状态联合概率密度演化方程。求解这一方程可分别得到非线性构形状态演化和结点力随机演化的概率结构。意味深长的是，非线性构形状态的演化方程可以直接由力-状态联合演化方程推导出来。而力的概率演化方程则不能实现力与状态之间的解耦。

Research on Evolution Probability of Forces by Vector Markov Method

In the present paper, a method was put forward to evaluate the evolution probability of the node force for memory-less structure under displacement-controlling loading. In the method, the force and nonlinear configuration state were combined to form a force-state compound vector Markov process. According to the separated analysis method, the state transition rates of probability were obtained firstly and then the joint probability evolution equation of the force-state compound vector Markov process could be set up. By solving the joint equations, the probability characteristic of evolution of the nonlinear configuration state and the node force could be evaluated. Furthermore, it is of significance that the evolution e-quations of the nonlinear configuration states can be deduced directly from the force-state joint evolution equations whereas the force and state can not be uncoupled in the evolution equations of the force.