A BRIEF ANALYSIS OF THE RELIABILITY OF TIME INTEGRATION METHOD IN UNSTABLE SYSTEMS

Based on the definitions of stability and attractiveness, the stability of linear time-invariant finite element discrete equations is discussed in three cases of eigenvalues. Employing the built-in power response module of the self-developed ZQFEM software, the algorithmic stability and computational accuracy of two time integration methods, Newmark-β and Wilson-θ, are verified in unstable linear time-invariant systems. Theoretical analysis shows that when the product of mass and damping is less than 0, the linear time-invariant system is unstable. The numerical analysis results indicate that the stability of the time integration method represented by Newmark-β and Wilson-θ is independent of the stability of the linear time invariant system; In the unstable linear time-invariant system, even if the displacement, velocity and acceleration are unbounded, the algorithm can obtain a high-precision numerical solution approaching the analytical solution by reducing the time step. The research results verify the reliability of the time integration method in unstable linear time-invariant systems, and have important reference value for the development of finite element software or the use of commercial software.