Time discontinuous finite element method for transient response analysis of linear time-varying structures

In this paper, a mixed form of Hamilton's law of variable mass system is proposed, and then a time discontinuous finite element method for transient response analysis of linear time-varying structures is developed based on the law. As these time-varying parameters are degraded into time-invariant ones, the time discontinuous finite element method for linear time-varying structures is degraded into an unconditionally stable higher-order accurate time integration method for linear time-invariant structures. The performance of the proposed time integration method has been verified and assessed extensively through many numerical examples, including the single-degree-of-freedom system with a time-varying mass and the string and beam structure with a moving mass. Numerical results demonstrate that the proposed time finite element method for linear time-varying structures performs extremely well compare with the Newmark method, the existing time continuous finite element method for linear time-varying structures as well as the combination of linear time-invariant time integration method and time frozen technique.