A family of single-step Houbolt time integration algorithms for structural dynamics Original Research Article

A new family of implicit, single-step time integration methods is presented for solving structural dynamics problems. The proposed method is unconditionally stable, second-order accurate and asymptotically annihilating. It is spectrally equivalent to Houboltʹs method but is cast in single-step form rather than multi-step form; thus the new algorithm computationally is more convnient. An explicit predictor-corrector algorithm is presented based upon new implicit scheme. The explicit algorithm is spectrally equivalent to the central difference method. The two new algorithms are merged into an implicit-explicit method, resulting in an improved algorithm for solving structural dynamics problems composed of ‘soft’ and ‘stiff’ domains. Numerical results are presented demonstrating the improved performance of the new implicit-explicit method compared to previously developed implicit-explicit schemes for structural dynamics.