Meshless thermal modeling and analysis of functionally graded materials using a meshless local moving kriging interpolation method

Abstract

In this study, meshless thermal analysis of functionally graded materials (FGM) is presented by using a meshless local moving kriging interpolation method. The method is developed based on local collocation with moving kriging shape function. It is truly meshless and having the Kronecker delta property for accurate imposition of boundary conditions. To improve its accuracy, the weight function is used with correlation parameter treated as the model internal length factor. This produces a meshless local method with clear meaning of model parameter, improved accuracy and allowing a more straightforward analysis for parametric study. Effects of weight function type, parameter value and number of supporting nodes to the method accuracy and convergence rate are first examined in a detailed parametric study of a benchmark problem. Based on the study, suitable parameter, weight function and effective range for supporting nodes number are elucidated. The proposed method is then applied for complex thermal analysis of FGM in arbitrary geometries, taking into account for both temperature and spatial dependent material properties and varied power-law index, including the presence of porosity as well. Numerical results show the effectiveness and accuracy of the meshless method for thermal modeling and analysis of FGM.