scholarly journals A Dual Reciprocity Time-Stepping BEM Applied to the Transient Heat Conduction Problem of Functionally Graded Materials.

2002 ◽  
Vol 68 (676) ◽  
pp. 1702-1707
Author(s):  
Masataka TANAKA ◽  
Toshiro MATSUMOTO ◽  
Yusuke SUDA ◽  
Susumu TAKAKUWA
Keyword(s):  
Heat Conduction ◽  
Functionally Graded Materials ◽  
Heat Conduction Problem ◽  
Transient Heat Conduction ◽  
Functionally Graded ◽  
Graded Materials ◽  
Time Stepping ◽  
Transient Heat Conduction Problem

Transient Heat Conduction in Functionally Graded Materials by LT-MFS

2011 ◽  
Vol 189-193 ◽  
pp. 1664-1669 ◽  
Author(s):  
Ning Zhao ◽  
Lei Lei Cao ◽  
Hui Guo
Keyword(s):  
Heat Conduction ◽  
Functionally Graded Materials ◽  
Heat Conduction Problem ◽  
Transient Heat Conduction ◽  
Fundamental Solutions ◽  
Functionally Graded ◽  
Time Variable ◽  
Graded Materials ◽  
Time Space ◽  
Transient Heat Conduction Problem

: The LT-MFS approach is proposed to solve two-dimensional transient heat conduction problem in functionally graded materials (FGMs). First, a Laplace transform approach is used to move the time variable. Then, a fundamental solution in Laplace space for FGMs is constructed. Next, the solution in Laplace space is approximated by the linear combination of fundamental solutions. Further, Stefest’s algorithm is employed to convert the results in Laplace space back into the time–space domain. Finally, the method is tested on several benchmark examples. The results demonstrate well the efficiency and accuracy of the proposed method.

scholarly journals Peridynamics Model with Surface Correction Near Insulated Cracks for Transient Heat Conduction in Functionally Graded Materials

Materials ◽  
2020 ◽  
Vol 13 (6) ◽  
pp. 1340
Author(s):  
Yang Tan ◽  
Qiwen Liu ◽  
Lianmeng Zhang ◽  
Lisheng Liu ◽  
Xin Lai
Keyword(s):  
Heat Conduction ◽  
Functionally Graded Materials ◽  
Surface Effect ◽  
Domain Boundary ◽  
Transient Heat Conduction ◽  
Functionally Graded ◽  
Classical Solutions ◽  
Graded Materials ◽  
Material Points ◽  
Surface Correction

A peridynamic (PD) model of functionally graded materials (FGMs) is presented to simulate transient heat conduction in the FGM plate with insulated cracks. The surface correction is considered in the model to reduce the surface effect near the domain boundary and insulated cracks. In order to verify the proposed model, a numerical example for the FGM plate is carried out. The results show good agreement with the analytical solution. The convergence of the model with the surface correction for FGMs without cracks is then investigated. The results reveal that our model converges to the classical solutions in the limit of the horizon going to zero. The effects of two material points discretization schemes on the accuracy of numerical results are investigated. For transient heat conduction of FGMs with a static crack, the results obtained from the proposed PD model agree well with that from the finite element method. Finally, transient heat conduction of the FGM plate with a dynamic horizontal crack and intersecting cracks is simulated and discussed.

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