An improved implicit‐explicit time integration method for structural dynamics

Abstract

SUMMARYAn explicit predictor-corrector algorithm is derived from the implicit a-method. This explicit algorithm is shown to have better stability and accuracy properties than its Newmark-based predecessor. This algorithm is then combined with the implicit a-method, resulting in an implicit-explicit a-method which can be effectively utilized for linear and non-linear structural dynamics calculations.

Explicit Predictor–multicorrector Time Discontinuous Galerkin Methods for Linear Dynamics

“…These results agree with the behaviour of other explicit predictor}corrector Newmark methods [14], [1, p. 562].…”

Seismic fracture analysis of concrete gravity dams including dam–reservoir interaction

“…(14) in the preceding section. Solution of this equation is carried out in time domain using the improved form of HHT-a integration method presented by Miranda et al [26]. The integration method retains the Newmark difference formulas: …”

“…The improved form of HHT-a time integration algorithm is given in Ref. [26]. If the solution at the time step i is known, the predicted displacement and velocity vectors for the time step i + 1 can be calculated as…”

A Stochastic Newmark Method for Engineering Dynamical Systems

“…Now, towards deriving the stochastic Newmark map over the ith time interval, the "rst step is to consider equation (2) and expand each element of the vectors X (t G\ #h)" X(t G\ #h) and X (t G\ #h)"X Q (t G\ #h) in a stochastic Taylor expansion around X (t G\ )"X G\ and X (t G\ )"X G\ respectively. In the present study, the derivation of the map is performed following Ito's formula, which, as adapted speci"cally for equation (2), is stated below:…”