Newmark积分方法在负刚度时的数值稳定性分析

On the stability of Newmark integration method for structure with negative stiffness

为了获得Newmark积分方法在负刚度时的适用性,研究了Newmark积分方法在负刚度时的数值稳定性分析方法并对其稳定性进行了分析,分析了Newmark积分方法中的参数、阻尼和分析步长对积分方法稳定性的影响规律.结果表明其稳定性与正刚度时差异较大,在负刚度时不再具有无条件稳定性.对于正刚度时常用的Newmark积分参数α=1/4、δ=1/2,在负刚度时仅当分析步长大于某一值时积分方法才能保证稳定性,因此难以同时满足稳定性和准确性的要求.推荐了通过选取合适的Newmark积分参数获得稳定性的方法.为Newmark积分方法用于分析具有负刚度的结构时的适用性提供了依据,也为积分方法的合理选择提供了参考.

To study the applicability of Newmark integration method for structure with negative stiffness,the method is first investigated,and then the numerical stability of the integration method is analyzed.The influ-ences of Newmark integration parameters,damping and time increment on numerical stability of Newmark inte-gration method are also discussed.The result shows that the integration method,which is very different from the case of positive stiffness,is not unconditional numerical stable in the case of negative stiffness.It is found that the usually used Newmark integration method in the case of positive stiffness with α=1/4,δ=1/2 is dif-ficult to achieve a balance between stability and accuracy because it is stable only when the time increment la-ger than a critical value in the case of negative stiffness.The strategy to obtain numerical stability is proposed by selecting appropriate Newmark integration parameters.This paper presents references for applicability of Newmark integration method and selection of rational integration method when structures with negative stiff-ness.