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An Introduction to Nonlinear Finite Element Analysis$
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J. N. Reddy

Print publication date: 2004

Print ISBN-13: 9780198525295

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198525295.001.0001

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Nonlinear Analysis of Time-Dependent Problems

Nonlinear Analysis of Time-Dependent Problems

Chapter:
(p.287) 8 Nonlinear Analysis of Time-Dependent Problems
Source:
An Introduction to Nonlinear Finite Element Analysis
Author(s):

J. N. REDDY

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198525295.003.0008

In this chapter, finite element models are used to solve time-dependent problems with nonlinearities and some standard time approximation schemes are described. All classes of nonlinear problems discussed in the previous chapters are revisited in the context of transient analysis, including heat transfer, flows of viscous incompressible fluids, and plate bending. The finite element formulation of time-dependent problems involves following two stages: spatial approximation and temporal approximation. All time approximation schemes are broadly classified as implicit and explicit. Parabolic equations, stability and accuracy of the finite element models, and computer implementation of the models are discussed. Numerical examples of linear and nonlinear problems are given.

Keywords:   finite element models, time-dependent problems, nonlinear problems, heat transfer, computer implementation, parabolic equations, time approximation schemes, plate bending, incompressible fluids

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