基于Gurtin变分原理的一种逐步积分法

Step by Step Integration Method Based on Gurtin Variational Principle

基于Gurtin变分原理,利用经过空间离散后的只含单重卷积形式的泛函,在局部时间域上采用初位移、初速度和末位移、末速度并加入一种非时间步参数的插值函数形式对时间域进行离散,给出了一种逐步积分法。文中通过对动力计算方法的稳定性研究,选取了合适的非时间步参数。精度分析和数值算例表明本文方法是一种可以应用于结构动力响应分析并具有较高精度的方法。

Based on Gurtin variational principle, a kind of new unconditional stable step by step integration method is presented. The method is given by firstly adopting a single convolution integral functional after spatial discretization operation, and then adopting interpolation functions of initial displacement, initial velocity,later instant displacement and later instant velocity with a non-time-step-parameter in them to approximate the nodal displacements within local time domain, An optimum value of non-time-step-parameter is evaluated through the stability analysis. Accuracy analysis and numerical examples show that the new algorithm possesses satisfying accuracy and is an effective method for the calculations of dynamic response in practical engineering.