An improved implicit method with dissipation control capability: The simple generalized composite time integration algorithm

In this paper, a simple and accurate implicit composite time integration scheme is newly developed for more efficient transient analyses of structural problems. The new scheme does not require the acceleration vector of the previous time step, and the initial acceleration vector is not needed, eithe...

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Bibliographic Details
Published in:Applied Mathematical Modelling Vol. 81; p. 910
Main Author: Kim, Wooram
Format: Journal Article
Language:English
Published: New York Elsevier BV 01.05.2020
Subjects:
Algorithms
Elastic bars
Implicit methods
Mass matrix
Pendulums
Stability
Time integration
Transient analysis
ISSN:1088-8691, 0307-904X
Online Access:Get full text
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Summary:In this paper, a simple and accurate implicit composite time integration scheme is newly developed for more efficient transient analyses of structural problems. The new scheme does not require the acceleration vector of the previous time step, and the initial acceleration vector is not needed, either. As a result, the factorization of the mass matrix is unnecessary, while factorizations of the effective coefficient matrix are still needed. Besides, the new method is designed to possess controllable algorithmic dissipation. Despite the absence of the acceleration vector of the previous time step, the numerical performance of the new method is equivalent to those of the existing methods. The excitation of an elastic bar problem and the simple nonlinear pendulum problem are numerically analyzed for the test of the new scheme. In the numerical experiments, the effects of consistent and lumped mass matrices are also discussed.
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ISSN:1088-8691
0307-904X
DOI:10.1016/j.apm.2020.01.043