Heat conduction analysis for irregular functionally graded material geometries using the meshless weighted least-square method with temperature-dependent material properties

This article presents the heat conduction analysis for irregular functionally graded material (FGM) with temperature-dependent material properties. For irregular FGM geometries, the meshless weighted least-square (MWLS) method is easy to model, implement, and interpolate those irregularly distributed field variables. To solve the heat conduction problem coupled with temperature-dependent FGM, the Laplace's equilibrium equation and boundary condition become nonlinear. Thus, the Kirchhoff transformation is employed to convert the nonlinear problem to linear solution. MWLS method as a pure meshless analysis is then used to solve the linear equation of FGM geometries. Next, the temperature field is obtained by the inverse Kirchhoff transformation. Finally, the accuracy and effectiveness of the method were demonstrated by several numerical cases.