An efficient hybrid boundary-type weak-form meshfree algorithm for 2D thermal analysis in inhomogeneous functionally graded materials

Exponential, quadratic, and trigonometric 2D thermal analysis in inhomogeneous functionally graded materials (FGMs) are solved through an efficient hybrid boundary-type weak-form meshfree algorithm, which is the virtual boundary meshfree Galerkin method with fundamental solutions (FS-VBMGM). Three types of temperature fundamental solutions for FGMs are introduced. The corresponding thermal flow fundamental solutions are derived in detail. Temperature and thermal flux are obtained by utilizing the virtual boundary element method (VBEM) based on the continuous virtual loads. The continuous virtual loads are constructed through the radial basis function interpolation (RBFI) of meshfree algorithm. Using the Galerkin method, calculating formula of FSVBMGM for thermal analysis in inhomogeneous FGMs is deducted. The benefits of VBEM, Galerkin method, and meshfree algorithm are thus presented in FS-VBMGM. Exponential, quadratic, and trigonometric inhomogeneous numerical examples of FGMs are calculated and contrasted to the exact solutions as well as other numerical methods. The reliability and exactness are proved. The specific discrete formula of FS-VBMGM for thermal analysis in inhomogeneous FGMs is simple to program and extended to calculate other particularly composite FGMs examples.