Numerical analysis of nonlinear dynamic structures frequently makes use of the central difference method to step the transient forward in time. The method is particularly robust, accommodating material and geometric nonlinearities as well as contact surfaces and constraints of a very general nature. The implementation of the method is most usually performed according to [1], where velocity terms (or more generally rate quantities) are taken half a time step from the displacement and acceleration terms. It was recognized that a proper check of energy balance, requires that velocity must also be interpolated to the integer steps [2]. The stability and accuracy of the central difference method is well established, and decades of experience including its use in numerous commercial finite element codes confirms why it is the method of choice for explicit time integration of transients.
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ASME 2008 Pressure Vessels and Piping Conference
July 27–31, 2008
Chicago, Illinois, USA
Conference Sponsors:
- Pressure Vessels and Piping
ISBN:
978-0-7918-4825-8
PROCEEDINGS PAPER
Second Order Errors Related to Geometric Nonlinearity in Explicit Central Difference Operator Available to Purchase
Don R. Metzger,
Don R. Metzger
Atomic Energy of Canada Limited, Mississauga, ON, Canada
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Young-Suk Kim
Young-Suk Kim
Atomic Energy of Canada Limited, Mississauga, ON, Canada
Search for other works by this author on:
Don R. Metzger
Atomic Energy of Canada Limited, Mississauga, ON, Canada
Young-Suk Kim
Atomic Energy of Canada Limited, Mississauga, ON, Canada
Paper No:
PVP2008-61618, pp. 335-340; 6 pages
Published Online:
July 24, 2009
Citation
Metzger, DR, & Kim, Y. "Second Order Errors Related to Geometric Nonlinearity in Explicit Central Difference Operator." Proceedings of the ASME 2008 Pressure Vessels and Piping Conference. Volume 2: Computer Applications/Technology and Bolted Joints. Chicago, Illinois, USA. July 27–31, 2008. pp. 335-340. ASME. https://doi.org/10.1115/PVP2008-61618
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