An alternative to the Bathe algorithm

This paper presents a new composite sub-steps algorithm for solving reliable numerical responses in structural dynamics. The newly developed algorithm is a two sub-steps, second-order accurate and unconditionally stable implicit algorithm with the same numerical properties as the Bathe algorithm. Th...

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Bibliographic Details
Published in:Applied Mathematical Modelling Vol. 69; p. 255
Main Authors: Li, Jinze, Yu, Kaiping
Format: Journal Article
Language:English
Published: New York Elsevier BV 01.05.2019
Subjects:
Algorithms
Lagrange multiplier
Stability analysis
Stiffness matrix
ISSN:1088-8691, 0307-904X
Online Access:Get full text
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Summary:This paper presents a new composite sub-steps algorithm for solving reliable numerical responses in structural dynamics. The newly developed algorithm is a two sub-steps, second-order accurate and unconditionally stable implicit algorithm with the same numerical properties as the Bathe algorithm. The detailed analysis of the stability and numerical accuracy is presented for the new algorithm, which shows that its numerical characteristics are identical to those of the Bathe algorithm. Hence, the new sub-steps scheme could be considered as an alternative to the Bathe algorithm. Meanwhile, the new algorithm possesses the following properties: (a) it produces the same accurate solutions as the Bathe algorithm for solving linear and nonlinear problems; (b) it does not involve any artificial parameters and additional variables, such as the Lagrange multipliers; (c) The identical effective stiffness matrices can be obtained inside two sub-steps; (d) it is a self-starting algorithm. Some numerical experiments are given to show the superiority of the new algorithm and the Bathe algorithm over the dissipative CH-α algorithm and the non-dissipative trapezoidal rule.
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ISSN:1088-8691
0307-904X
DOI:10.1016/j.apm.2018.12.027