Two families of dual-explicit model-based integration algorithms with controllable numerical damping for structural dynamic problems - Fu, Bo; Lavery Ilunga, Stephane; Chen, Jin (Mechanical systems and signal processing, 2024)
Based on the recently proposed multi-sub-step implicit β1/β2-Bathe method and a novel mapping strategy on the error equation, this paper presents two families of dual-explicit model-based integration algorithms for solving linear and nonlinear dynamic problems. Firstly, the dual-explicit formulations of the well-known Chen and Ricles (CR) algorithm are adopted for the new algorithms. By matching the error equations of the new algorithms and the implicit β1/β2-Bathe method, the model-based integration parameters of the new algorithms are then derived. After analyzing the numerical properties of the two algorithms, it can be found that they are unconditionally stable for linear and nonlinear softening dynamic problems when the governing integration parameters are within specific ranges. Besides the two algorithms’ numerical dispersion and energy dissipation are identical to the parent algorithm, i.e., the β1/β2-Bathe method. The overshooting issue of the proposed algorithms is less prominent than in some representative model-based algorithms. Finally, two numerical examples are used to investigate the computational efficiency and accuracy of the new algorithms compared to the parent algorithm and some existing model-based algorithms, including those with controllable damping, i.e., the KR-α and MKR-α methods. The results show that the two families of new algorithms are less computationally expensive than the parent algorithm as they adopt dual-explicit and single-step formulation. In addition, it is also observed that the developed algorithms have a better performance of damping out the spurious effect at high modes than the KR-α and MKR-α methods.