结构动力响应数值算法耗散和超调特性设计

对结构动力响应数值计算问题提出引入多个自由参数来获得所希望的算法特性. 多参数的一个明显的好处就是在算法设计上有更大的自由空间. 利用这些自由参数获得了两个新的无条件稳定、有二阶精度的、有好的耗散和没有超调的单步时间直接积分算法. 在存在阻尼情况下基于有限差分分析理论证明了新算法的这些特性. 其中一个有高频渐进消去特性，且在有阻尼情况下与Houbolt方法相比对高频有更强的耗散. 另一个在低频极限无耗散，高频耗散可以用一自由参数控制. 超调分析结果显示两个新算法都不显示超调，而HHT方法不仅有速度超调，还有位移超调. 最后使用一些算例并通过与传统方法的比较数值地验证了理论分析结果.

Two time integral algorithms with numerical dissipation and without overshoot for structural dynamic

The seven free parameters were introduced into the governing equation of a motion to design new direct integral algorithms for solving structural dynamics problems. Two new one-step schemes were presented by selecting free parameters in the process of algorithmic finite difference analysis. The proposed methods are implicit, unconditionally stable, second-order accurate, numerically dissipative, and no overshot. One of the algorithms is able to annihilate the high-frequency modes asymptotically, and is more dissipative than Houbolt method for damped system. The numerical dissipation of the other method is minimum in the low-frequency regime and is controllable in the high-frequency regime. An analysis of the overshoot property is directly performed for damped system and show that proposed two algorithms no exhibits overshoot, while the HHT-a scheme suffers from the displacement and velocity overshoot simultaneously when damping existed. Finally, the results of the analysis were validated numerically by the comparison with the Newmark, HHT-a and Houbolt methods by analyzing a simulated two degree-of-freedom system representing a large structural.