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A family of single-step Houbolt time integration algorithms for structural dynamics. (English) Zbl 0849.73079
Summary: 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 Houbolt’s method but is cast in single-step form rather than multistep form; thus the new algorithm computationally is more convenient. An explicit predictor-corrector algorithm is presented based upon the 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.

MSC:
74S20 Finite difference methods applied to problems in solid mechanics
74H45 Vibrations in dynamical problems in solid mechanics
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