MLS-based numerical manifold method for steady-state three-dimensional heat conduction problems of functionally graded materials

Abstract

In this study, the moving least squares based numerical manifold method (MLS-NMM) is firstly applied to discretize three-dimensional (3D) steady heat conduction problems of functionally graded materials (FGMs). In the 3D MLS-NMM, the influence domains of nodes in the moving least squares (MLS) are used as the mathematical patches to construct the mathematical cover (MC); while the shape functions of MLS-nodes as the weight functions subordinate to the MC. Compared with the traditional NMM using finite elements to form the MC, the cutting operations in generating the physical cover are unnecessary and the computation complexity is decreased significantly. Based on the Galerkin method, the discrete form of 3D heat conduction is derived. Finally, a series of numerical experiments concerning steady heat conduction problems are performed, suggesting that the proposed MLS-NMM enjoys advantages of both MLS and NMM in solving steady heat conduction.