Development of Direct Integration Algorithms for Structural Dynamics Using Discrete Control Theory
Publication: Journal of Engineering Mechanics
Volume 134, Issue 8
Abstract
In structural dynamics, integration algorithms are often used to obtain the solution of temporally discretized equations of motion at selected time steps. Various time integration algorithms have been developed in the time domain using different methods. In order for an integration algorithm to be reliable it must be stable and accurate. A discrete transfer function is used to study the properties of integration algorithms. A pole mapping rule from control theory in conjunction with a discrete transfer function is used to develop new integration algorithms for obtaining solutions to structural dynamics problems. A new explicit integration algorithm, called the CR (Chen and Ricles) algorithm, is subsequently developed based on the proposed method. The properties of the algorithm are investigated and compared with other well established algorithms such as the Newmark family of integration algorithms. By assigning proper stable poles to the discrete transfer function the newly developed CR explicit algorithm is unconditionally stable and has the same accuracy as the Newmark method with constant acceleration. In addition, the CR algorithm is based on expressions for displacement and velocity that are both explicit in form, making it an appealing integration algorithm for solving structural dynamics problems.
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Acknowledgments
This paper is based upon work supported by a grant from the Pennsylvania Department of Community and Economic Development through the Pennsylvania Infrastructure Technical Alliance, and by the National Science Foundation (NSF) under Grant No. NSFCMS-0402490 within the George E. Brown, Jr. Network for Earthquake Engineering Simulation Consortium Operation. Their support is gratefully appreciated. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the writers and do not necessarily reflect the views of the sponsors.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 134 • Issue 8 • August 2008
Pages: 676 - 683
Copyright
© 2008 ASCE.
History
Received: Nov 27, 2006
Accepted: Feb 4, 2008
Published online: Aug 1, 2008
Published in print: Aug 2008
Notes
Note. Associate Editor: Lambros S. Katafygiotis
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