Energy conserving balance of explicit time steps to combine implicit and explicit algorithms in structural dynamics

Recent developments have proved the advantage of combining both time implicit and time explicit integration algorithms in structural dynamics. A major problem is to define the initial conditions for the implicit simulation on the basis of a solution obtained from an unbalanced explicit resolution. The unbalanced nature of the explicit algorithm leads to oscillations in the fields of interest. Therefore, the values obtained after an explicit computation cannot be used directly as initial conditions for an implicit simulation. In this paper, we develop such initial values that lead to a stable (no numerical creation of energy) and energy-conserving transition.