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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 Two Dimensions

Heat Transfer and Other Field Problems in Two Dimensions

(p.127) 5 Heat Transfer and Other Field Problems in Two Dimensions
An Introduction to Nonlinear Finite Element Analysis


Oxford University Press

This chapter considers the use of the finite element method in analysing problems in which the coefficients of the differential equation are possibly functions of the dependent variable and its derivatives. The focus is on heat transfer and other two-dimensional problems. A representative element domain is used to derive the weak form of the model equation, with the assumption that each element has a unique geometric shape and associated interpolation functions. Solution procedures are examined, including direct iteration and Newton-Raphson iteration, along with computer implementation of the process.

Keywords:   finite element method, heat transfer, two-dimensional problems, differential equation, direct iteration, Newton-Raphson iteration, computer implementation

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