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

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.