TY - JOUR
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
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U2 - 10.1016/j.cma.2004.02.018
DO - 10.1016/j.cma.2004.02.018
M3 - Article
AN - SCOPUS:10044250030
SN - 0374-2830
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 -