结构时程响应分析的Hermite-配点积分法

A Hermite-Collocation Integration Method for Dynamic Response Analysis of Structures

本文给出了结构动力运动方程的一种单数值积分的计算格式。本文以Hermite插值函数作为时域的位移函数,应用配点法,在时间步长中令运动方程的加权钱数为零,推导出带有参数θ,且精度较高的计算格式。当参数θ满足0.5<θ<1时,本文的计算格式是无条件稳定的。在考虑阻尼的情况下,当0.35<θ≤0.5时,格式也同样是无条件稳定的,而且精度的三项指标AD,PE和■都优于Wilson-θ法和Newmark法。本文还通过例题进一步验证了计算格式的精度较上述方法高,能更好地与精确解相吻合。

In this paper, a single-step numerical integration algorithm for the dynamic response analysis of structures is proposed. By means of collocation method using Hermite interpolation function as the displacement fanction in time domain and putting yero residuals in the motion differential equations of structure at two time moments in one time step, a higher accuracy calculation scheme with a parameter θ will be obtained. The analysis of stability and accuracy of the scheme are prosented. The scheme is unconditionally stable within the range of 0.5<θ<1. In the case of 0.3<θ≤0.5, the damping is considered, the scheme can be also unconditionally stable. The accuracy of the scheme as measured by AD, PE and is better than that of the wilson-θ method and Newmark method. Examples show that the result of the scheme is more close to the exact solution than wilson-θ method.