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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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Heat Transfer and Other Field Problems in One Dimension

Heat Transfer and Other Field Problems in One Dimension

Chapter:
(p.61) 3 Heat Transfer and Other Field Problems in One Dimension
Source:
An Introduction to Nonlinear Finite Element Analysis
Author(s):

J. N. REDDY

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198525295.003.0003

This chapter considers the use of the finite element method in analysing heat transfer and other field problems in one dimension. A model nonlinear differential equation governing one-dimensional problems involving a single unknown is presented to illustrate the finite element model development and discuss solution methods to solve the resulting nonlinear algebraic equations. In this case, iterative methods must be used to solve the nonlinear finite element equations. The direct iteration procedure and Newton's iteration procedure are discussed, along with the computer implementation of the finite element method.

Keywords:   finite element method, heat transfer, one-dimensional problems, nonlinear differential equation, iteration procedure, computer implementation

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