The simple boundary element method for transient heat conduction in functionally graded materials

Alok Sutradhar; Glaucio H. Paulino

doi:10.1016/j.cma.2004.02.018

The simple boundary element method for transient heat conduction in functionally graded materials

Alok Sutradhar
, Glaucio H. Paulino

Research output: Contribution to journal › Article › peer-review

184 Scopus citations

Abstract

This paper presents a "simple" boundary element method for transient heat conduction in functionally graded materials, which leads to a boundary-only formulation without any domain discretization. For a broad range of functional material variation (quadratic, exponential and trigonometric) of thermal conductivity and specific heat, the non-homogeneous problem can be transformed into the standard homogeneous diffusion problem. A three-dimensional boundary element implementation, using the Laplace transform approach and the Galerkin approximation, is presented. The time dependence is restored by numerically inverting the Laplace transform by means of the Stehfest algorithm. A number of numerical examples demonstrate the efficiency of the method. The results of the test examples are in excellent agreement with analytical solutions and finite element simulation results.

Original language	English (US)
Pages (from-to)	4511-4539
Number of pages	29
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	193
Issue number	42-44
DOIs	https://doi.org/10.1016/j.cma.2004.02.018
State	Published - Oct 22 2004
Externally published	Yes

All Science Journal Classification (ASJC) codes

Computational Mechanics
Mechanics of Materials
Mechanical Engineering
General Physics and Astronomy
Computer Science Applications

Keywords

Boundary element method
Functionally graded materials
Galerkin
Green's function
Non-homogeneous materials
Three-dimensional analysis
Transient heat conduction

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10.1016/j.cma.2004.02.018

Cite this

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title = "The simple boundary element method for transient heat conduction in functionally graded materials",

abstract = "This paper presents a {"}simple{"} boundary element method for transient heat conduction in functionally graded materials, which leads to a boundary-only formulation without any domain discretization. For a broad range of functional material variation (quadratic, exponential and trigonometric) of thermal conductivity and specific heat, the non-homogeneous problem can be transformed into the standard homogeneous diffusion problem. A three-dimensional boundary element implementation, using the Laplace transform approach and the Galerkin approximation, is presented. The time dependence is restored by numerically inverting the Laplace transform by means of the Stehfest algorithm. A number of numerical examples demonstrate the efficiency of the method. The results of the test examples are in excellent agreement with analytical solutions and finite element simulation results.",

keywords = "Boundary element method, Functionally graded materials, Galerkin, Green's function, Non-homogeneous materials, Three-dimensional analysis, Transient heat conduction",

author = "Alok Sutradhar and Paulino, \{Glaucio H.\}",

note = "Funding Information: We acknowledge the support from the Computational Science and Engineering (CSE) Program (Prof. Michael Heath, Director) at the University of Illinois at Urbana-Champaign (UIUC) for the CSE Fellowship award to A. Sutradhar. G.H. Paulino acknowledges the support from the National Science Foundation under grant CMS-0115954 (Mechanics and Materials Program). ",

year = "2004",

month = oct,

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doi = "10.1016/j.cma.2004.02.018",

language = "English (US)",

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T1 - The simple boundary element method for transient heat conduction in functionally graded materials

AU - Sutradhar, Alok

AU - Paulino, Glaucio H.

N1 - Funding Information: We acknowledge the support from the Computational Science and Engineering (CSE) Program (Prof. Michael Heath, Director) at the University of Illinois at Urbana-Champaign (UIUC) for the CSE Fellowship award to A. Sutradhar. G.H. Paulino acknowledges the support from the National Science Foundation under grant CMS-0115954 (Mechanics and Materials Program).

PY - 2004/10/22

Y1 - 2004/10/22

N2 - This paper presents a "simple" boundary element method for transient heat conduction in functionally graded materials, which leads to a boundary-only formulation without any domain discretization. For a broad range of functional material variation (quadratic, exponential and trigonometric) of thermal conductivity and specific heat, the non-homogeneous problem can be transformed into the standard homogeneous diffusion problem. A three-dimensional boundary element implementation, using the Laplace transform approach and the Galerkin approximation, is presented. The time dependence is restored by numerically inverting the Laplace transform by means of the Stehfest algorithm. A number of numerical examples demonstrate the efficiency of the method. The results of the test examples are in excellent agreement with analytical solutions and finite element simulation results.

AB - This paper presents a "simple" boundary element method for transient heat conduction in functionally graded materials, which leads to a boundary-only formulation without any domain discretization. For a broad range of functional material variation (quadratic, exponential and trigonometric) of thermal conductivity and specific heat, the non-homogeneous problem can be transformed into the standard homogeneous diffusion problem. A three-dimensional boundary element implementation, using the Laplace transform approach and the Galerkin approximation, is presented. The time dependence is restored by numerically inverting the Laplace transform by means of the Stehfest algorithm. A number of numerical examples demonstrate the efficiency of the method. The results of the test examples are in excellent agreement with analytical solutions and finite element simulation results.

KW - Boundary element method

KW - Functionally graded materials

KW - Galerkin

KW - Green's function

KW - Non-homogeneous materials

KW - Three-dimensional analysis

KW - Transient heat conduction

UR - https://www.scopus.com/pages/publications/10044250030

UR - https://www.scopus.com/pages/publications/10044250030#tab=citedBy

U2 - 10.1016/j.cma.2004.02.018

DO - 10.1016/j.cma.2004.02.018

M3 - Article

AN - SCOPUS:10044250030

SN - 0045-7825

VL - 193

SP - 4511

EP - 4539

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

IS - 42-44

ER -

The simple boundary element method for transient heat conduction in functionally graded materials

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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