Abstract
Nearly all the methods one encounters in mechanics for solving nonlinear evolution problems are incremental methods. The load, or rather the interval of time [0, T] considered, is decomposed into a succession of (generally) small intervals. The history of different quantities being known until the present instant t, one studies a new interval of time [ t, t + Δt] where Δt is the increment. The problem is then to determine the history on the interval [t, t + Δt]. In assuming, for example, a linear history on [t, t + Δt] that is, a history that depends only on values at the instant t + Δt we are led to a classical nonlinear problem where the time does not enter. This problem, which determines various quantities at time t + Δt is generally treated by a Newton-type method. We note that the only mechanics property used is the principle of causality.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media New York
About this chapter
Cite this chapter
Ladevèze, P. (1999). Solution Methods for Nonlinear Evolution Problems. In: Nonlinear Computational Structural Mechanics. Mechanical Engineering Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1432-8_3
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1432-8_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7141-3
Online ISBN: 978-1-4612-1432-8
eBook Packages: Springer Book Archive