On a fourth order FEA multistep time integration method for lightly damped media

For time integration in finite element analysis, a higher order counterpart of the widely used Newmark method is formulated by applying the three step fourth order Adams-Moulton (AM) method to lightly damped systems with accelerations. A linear system arises for which the solution effort is exactly the same as in Newmark. Using Pade approximations, step-wise and cumulative errors in both methods are assessed for both free and forced response. For comparable accuracy Newmark requires much smaller time steps than AM, even in low frequency modes. Numerical damping at fourth order is introduced into AM. Newmark is numerically stable for all time steps. However, owing to extraneous eigenvalues AM exhibits a critical ratio of time step to period, above which numerical instability occurs. This is problematic in high frequency modes with small time periods. It is shown that this stability limit is not obviated by damping, whether viscous or `numerical'. Instead, a discussion is given of removal of higher order modes using filters based on the Wavelet Transform.