A weighted residual parabolic acceleration time integration method for problems in structural dynamics
Abstract
In the proposed method, the variation of displacement in each time step
is assumed to be a fourth order polynomial in time and its five unknown coefficients are
calculated based on: two initial conditions from the previous time step; satisfying the
equation of motion at both ends of the time step; and the zero weighted residual within
the time step. This method is non-dissipative and its dispersion is considerably less
than in other popular methods. The stability of the method shows that the critical time
step is more than twice of that for the linear acceleration method and its convergence
is of fourth order.