非线性结构动力方程求解的显式差分格式的特性分析

本文针对软化非线性结构体系动力方程,分析了作者推导出的求解方程的显式差分格式的收敛性及稳定性,分别给出了结构体系处于非线性正刚度及屈服后的负刚度反应阶段时显式差分格式的稳定条件。稳定性分析结果表明,只要结构体系处于初始反应的粘-弹性阶段时显式差分格式满足稳定性条件,则可以保证软化非线性结构体系反应求解的整个过程中格式的计算稳定性。

THE ANALYSIS OF THE PROPERTIES OF AN EXPLICIT DIFFERENCE METHOD FOR SOLVING THE NONLINEAR STRUCTURAL DYNAMIC EQUATIONS

On the dynamic equations of the softening nonlinear structural system, the convergence and stability of an explicit difference method presented by authors for solving the dynamic equations are analysedin this paper, and the stability conditions are given when the structural system is under the nonlinear positive stiffness state and the negative post-yield stiffness state. The results of the stability analysis show that as long as the stability condition is satisfied when the structuralsystem is under the visco-elastic state at the beginning of the structural response, the stability will be ensured in the whole process of integrating the response of the softening nonlinear structural system.