Enhanced studies on the composite sub-step algorithm for structural dynamics: The Bathe-like algorithm

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 algor...

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Bibliographic Details
Published in:Applied Mathematical Modelling Vol. 80; p. 33
Main Authors: Li, Jinze, Li, Xiangyang, Yu, Kaiping
Format: Journal Article
Language:English
Published: New York Elsevier BV 01.04.2020
Subjects:
Algorithms
Approximation
Dynamic structural analysis
Parameters
Pendulums
ISSN:1088-8691, 0307-904X
Online Access:Get full text
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Summary: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.
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ISSN:1088-8691
0307-904X
DOI:10.1016/j.apm.2019.11.033