1. Enhanced studies on the composite sub-step algorithm for structural dynamics: The Bathe-like algorithm.
- Author
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Li, Jinze, Li, Xiangyang, and Yu, Kaiping
- Subjects
- *
STRUCTURAL dynamics , *NONLINEAR equations , *ALGORITHMS - Abstract
• Further studies on the Bathe algorithm is given and hence a novel class of the Bathe-like algorithm is presented. • It provides a new family of algorithms with the optimal numerical characteristics. • It gives a novel family of algorithms, which can be regarded as the alternative to the original Bathe algorithm. • This study shows that the Bathe algorithm can reduce to the trapezoidal rule and the backward Euler formula. The Bathe algorithm is superior to the trapezoidal rule in solving nonlinear problems involving large deformations and long-time durations. Generally, the parameter γ = 2 − 2 is highly recommended due to its optimal numerical properties. This paper further studies this implicit composite sub-step algorithm and thus presents a class of the Bathe-like algorithm. It not only gives a novel family of composite algorithms whose numerical properties are the exactly same as the original Bathe algorithm with γ = 2 − 2 , but also provides the generalized alternative to the original Bathe algorithm with any γ. In this study, it has been shown that the Bathe-like algorithm, including the original Bathe algorithm, can reduce to two common single-step algorithms: the trapezoidal rule and the backward Euler formula. Besides, a new parameter called the algorithmic mode truncation factor is firstly defined to describe the numerical property of the Bathe-like algorithm and it can estimate which modes to be damped out. Finally, numerical experiments are provided to show the superiority of the Bathe-like algorithm over some existing methods. For example, the novel Bathe-like algorithms are superior to the original Bathe algorithm when solving the highly nonlinear pendulum. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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