| New dissipative time integration algorithms are presented for solving systems of second-order ordinary differential equations that typically arise from the spatial discretization of elastodynamics problems. The new algorithms are: (1) a family of implicit generalized-;The implicit generalized-;The explicit generalized-;The implicit single-step Houbolt method is unconditionally stable, second-order accurate and asymptotically annihilating. It is spectrally equivalent to Houbolt's method but is cast in the more convenient single-step form rather than multi-step form. An explicit predictor-corrector algorithm based upon the new implicit scheme is spectrally equivalent to the central difference method. The two algorithms are merged into an implicit-explicit method, resulting in an improved algorithm for solving structural dynamics problems composed of "soft" and "stiff" domains. |
