Boundary element methods for axisymmetric heat conduction and thermoelastic deformations in nonhomogeneous solids

This thesis is concerned with the development of boundary element techniques for the numerical solution of several important classes of axisymmetric heat conduction and thermoelastic problems involving nonhomogeneous solids with material properties that vary continuously in space. The problems under...

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Main Author: Yun, Bao Ing
Other Authors: Ang Whye Teong
Format: Theses and Dissertations
Language:English
Published: 2013
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Online Access:https://hdl.handle.net/10356/51102
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-511022023-03-11T17:57:50Z Boundary element methods for axisymmetric heat conduction and thermoelastic deformations in nonhomogeneous solids Yun, Bao Ing Ang Whye Teong School of Mechanical and Aerospace Engineering DRNTU::Engineering::Mechanical engineering::Mechanics and dynamics This thesis is concerned with the development of boundary element techniques for the numerical solution of several important classes of axisymmetric heat conduction and thermoelastic problems involving nonhomogeneous solids with material properties that vary continuously in space. The problems under consideration have applications in the analyses of functionally graded materials which play an important role in engineering. The classes of axisymmetric problems considered in this thesis may be categorized as follows: (a) nonsteady heat conduction in a nonhomogeneous solid with temperature dependent material properties, (b) nonclassical heat conduction, based on the dual-phase-lag heat conduction model, in a nonhomogeneous solid, and (c) thermoelastostatic and thermoelastodynamic deformations in nonhomogeneous solids. The problems are formulated in terms of boundary-domain integral equations. The dual-reciprocity method is applied to transform approximately the domain integrals in the boundary-domain integral equations into boundary integrals. New axisymmetric interpolating functions, which are bounded in the axisymmetric coordinate plane but are expressed in terms of relatively simple elementary functions, are proposed for use in the dual-reciprocity method. In the last part of the thesis, an alternative boundary element approach, based on the theory of complex variables, is proposed for solving an axisymmetric problem involving steady heat conduction in a nonhomogeneous solid. With the aid of the axisymmetric interpolating functions, the problem is recast into one requiring the construction of a complex function which is analytic in the axisymmetric solution domain and which is such that the relevant boundary conditions are satisfied. Cauchy integral formulae are discretized to obtain a boundary element procedure for constructing the required complex function numerically. Unlike the real boundary element approach for axisymmetric problems, the complex variable approach does not require the evaluation of complicated fundamental solutions involving elliptic integrals. To check the validity of all the boundary element procedures, they are applied to solve specific problems with known analytical solutions. The numerical results obtained agree well with the analytical solutions. New results are also obtained for some problems which may be of some practical interest, such as axisymmetric laser heating of particular functionally graded solids. DOCTOR OF PHILOSOPHY (MAE) 2013-01-14T03:35:51Z 2013-01-14T03:35:51Z 2012 2012 Thesis Yun, B. I. (2012). Boundary element methods for axisymmetric heat conduction and thermoelastic deformations in nonhomogeneous solids. Doctoral thesis, Nanyang Technological University, Singapore. https://hdl.handle.net/10356/51102 10.32657/10356/51102 en 225 p. application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic DRNTU::Engineering::Mechanical engineering::Mechanics and dynamics
spellingShingle DRNTU::Engineering::Mechanical engineering::Mechanics and dynamics
Yun, Bao Ing
Boundary element methods for axisymmetric heat conduction and thermoelastic deformations in nonhomogeneous solids
description This thesis is concerned with the development of boundary element techniques for the numerical solution of several important classes of axisymmetric heat conduction and thermoelastic problems involving nonhomogeneous solids with material properties that vary continuously in space. The problems under consideration have applications in the analyses of functionally graded materials which play an important role in engineering. The classes of axisymmetric problems considered in this thesis may be categorized as follows: (a) nonsteady heat conduction in a nonhomogeneous solid with temperature dependent material properties, (b) nonclassical heat conduction, based on the dual-phase-lag heat conduction model, in a nonhomogeneous solid, and (c) thermoelastostatic and thermoelastodynamic deformations in nonhomogeneous solids. The problems are formulated in terms of boundary-domain integral equations. The dual-reciprocity method is applied to transform approximately the domain integrals in the boundary-domain integral equations into boundary integrals. New axisymmetric interpolating functions, which are bounded in the axisymmetric coordinate plane but are expressed in terms of relatively simple elementary functions, are proposed for use in the dual-reciprocity method. In the last part of the thesis, an alternative boundary element approach, based on the theory of complex variables, is proposed for solving an axisymmetric problem involving steady heat conduction in a nonhomogeneous solid. With the aid of the axisymmetric interpolating functions, the problem is recast into one requiring the construction of a complex function which is analytic in the axisymmetric solution domain and which is such that the relevant boundary conditions are satisfied. Cauchy integral formulae are discretized to obtain a boundary element procedure for constructing the required complex function numerically. Unlike the real boundary element approach for axisymmetric problems, the complex variable approach does not require the evaluation of complicated fundamental solutions involving elliptic integrals. To check the validity of all the boundary element procedures, they are applied to solve specific problems with known analytical solutions. The numerical results obtained agree well with the analytical solutions. New results are also obtained for some problems which may be of some practical interest, such as axisymmetric laser heating of particular functionally graded solids.
author2 Ang Whye Teong
author_facet Ang Whye Teong
Yun, Bao Ing
format Theses and Dissertations
author Yun, Bao Ing
author_sort Yun, Bao Ing
title Boundary element methods for axisymmetric heat conduction and thermoelastic deformations in nonhomogeneous solids
title_short Boundary element methods for axisymmetric heat conduction and thermoelastic deformations in nonhomogeneous solids
title_full Boundary element methods for axisymmetric heat conduction and thermoelastic deformations in nonhomogeneous solids
title_fullStr Boundary element methods for axisymmetric heat conduction and thermoelastic deformations in nonhomogeneous solids
title_full_unstemmed Boundary element methods for axisymmetric heat conduction and thermoelastic deformations in nonhomogeneous solids
title_sort boundary element methods for axisymmetric heat conduction and thermoelastic deformations in nonhomogeneous solids
publishDate 2013
url https://hdl.handle.net/10356/51102
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