The generalization of diagonally implicit Runge–Kutta–Nyström method with controllable numerical dissipation for structural dynamics

This paper strictly focuses upon novel designs of the time-integration algorithms as applied to structural dynamics systems with or without physical damping. The significant advances and contributions are summarized as follows: (1) the identity between the composite time-integration algorithms and t...

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Vydáno v:Nonlinear dynamics Ročník 112; číslo 1; s. 525 - 559
Hlavní autoři: Wang, Yazhou, Xue, Xiaodai, Wang, Tao, Xie, Ningning, Jia, Hongjin, Hu, Zhubing, Tamma, Kumar
Médium: Journal Article
Jazyk:angličtina
Vydáno: Dordrecht Springer Netherlands 01.01.2024
Springer Nature B.V
Témata:
Algorithms
Automotive Engineering
Classical Mechanics
Control
Controllability
Damping
Design optimization
Design parameters
Dynamic structural analysis
Dynamical Systems
Engineering
Mechanical Engineering
Nonlinear dynamics
Numerical dissipation
Original Paper
Roots
Runge-Kutta method
Time integration
Vibration
Runge–Kutta–Nyström method
Composite time integration
Controllable numerical dissipation
BN-stability
Structural dynamics and second-order systems
ISSN:0924-090X, 1573-269X
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Shrnutí:This paper strictly focuses upon novel designs of the time-integration algorithms as applied to structural dynamics systems with or without physical damping. The significant advances and contributions are summarized as follows: (1) the identity between the composite time-integration algorithms and the diagonally implicit Runge–Kutta family of algorithms are specifically established and demonstrated in order to clarify the originality, development, contribution, and pros/cons of the composite time-integration algorithms developed over the recent decades; (2) then, it is pointed out that the design of potential next-generation multi-stage time-integration algorithms with improved numerical properties can directly emanate from and already exist within the diagonally implicit Runge–Kutta–Nyström (DIRKN) computational framework itself, unlike composite-type time-integration methods paying efforts and attempting to design new algorithmic structures, although they are identical to and pertain primarily to the existing RK-type variants; (3) one- and two-stage DIRKN family of new algorithms and novel designs are taken into consideration for the first time, leading to novel sets of parameters with different numerical properties, which not only encompass existing methods by assigning two identical principal roots, but also produce new and novel designs by employing altogether distinctive principal roots; and finally, (4) the much coveted BN-stability feature and condition are additionally achieved and taken into consideration in order to optimize the design of parameters, which is competitive for nonlinear structural dynamics. Numerical examples are demonstrated to validate the analysis, new designs and the proposed overall efforts.
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ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-023-09065-7