A dual-explicit model-based integration algorithm with higher-order accuracy for structural dynamics

• Published in: Applied mathematical modelling 2022-10, Vol.110, p.513-541
• Main Authors: Fu, Bo, Zhang, Fu-Tai
• Format: Article
• Language: English
• Subjects: Accuracy; Explicit; Integration algorithm; Model-based; Period elongation; Structural dynamics
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2022.06.005

•The new algorithm is explicit for both displacement and velocity.•The new algorithm is unconditionally stable for linear and nonlinear softening stiffness systems.•The new algorithm has extremely small period error.•The new algorithm has no energy dissipation.•There still exist overshoot of the new algorithm. Several model-based or structure-dependent integration algorithms with explicit displacement formulation and unconditional stability are recently developed. According to the difference equations, these algorithms can be divided into dual-explicit and semi-explicit, where the first category algorithms are explicit for both displacement and velocity, while the second category are only explicit for displacement. The well-known Chen-Ricles (CR) and Chang algorithms are two representatives of dual-explicit and semi-explicit model-based algorithms, respectively. The model-based integration algorithms are promising with excellent computing efficiency, but most of them are second-order accurate. In this paper, a new dual-explicit (NDE) algorithm with higher-order accuracy is developed. The integration parameters of the NDE algorithm are obtained by using the pole mapping and second-order Pade approximation. Numerous important numerical characteristics including the consistency and local truncation error, stability, numerical dispersion and energy dissipation and overshoot are systematically analyzed for the new algorithm. It is found that the NDE algorithm is fourth-order accurate for free vibration without damping. As for forced vibration with/without damping and free vibration with damping, the NDE algorithm is no longer fourth-order accurate, but it is still more accurate than the CR and Chang algorithms. In addition, the period error of the algorithm is extremely small. Three representative numerical examples are finally provided to demonstrate the high accuracy of the NDE algorithm. Several classical and latest model-based integration algorithms and three fourth-order accurate algorithms are also adopted for comparisons. It has been proved that the NDE algorithm has much better performance than other selected model-based algorithms.