Search

The particular and homogeneous solutions of two-dimension (2D) thermal-elastic problems are expressed by using the virtual boundary element method (VBEM) and the superposition principle. Accordingly, two matrix equations are needed and formed for particular and homogeneous solutions by the novel nonsingular boundary element method with the radial basis function interpolation (RBFI), namely virtual boundary meshfree Galerkin method (VBMGM). Considering the boundary conditions of heat conduction and combining the Galerkin method, virtual source functions of particular solutions can be solved by first using VBMGM. Applying boundary conditions of transformation, virtual source functions of homogeneous solutions can be obtained by second employing VBMGM. The coefficients of two matrix equations are symmetrical. Formed equations are nonsingular and have merits of virtual boundary element method, meshfree method, and Galerkin method. The detailed expressions, calculation steps, and simplified flow chart are given in detail, that is convenient for other scholars to study other more complex thermo-elastic problems through the method of this paper. Three examples are calculated. Comparing their calculation results with other methods, the stability and the precision of VBMGM for 2D thermal-elastic problems are validated. [ABSTRACT FROM AUTHOR]

The virtual boundary meshfree Galerkin method (VBMGM) is demonstrated to solve the single-domain transient heat conduction with heat source problem. Both the heat source in the computational domain and the virtual source function on the virtual boundary are interpolated by using the radial basis function interpolation. The equation of the proposed method is formed by the Galerkin method. Consequently, VBMGM have the advantages of the Galerkin method, the boundary element method and the meshfree method for the single-domain transient heat conduction with heat source problem. And the numerical definitions of the weighted values in VBMGM are definite, such as the partial derivatives of the temperature, the heat flux and the heat source expression at t + Δ t time. The detailed equation of VBMGM is deducted for the single-domain transient heat conduction with heat source problem. Two numerical examples, the square domain with constant heat source and the square domain with variable boundary condition and variable heat source, are presented. The accuracy and the stability of VBMGM for the single-domain transient heat conduction with heat source problem are proved. [ABSTRACT FROM AUTHOR]

Virtual boundary meshfree Galerkin method (VBMGM) is developed to solve the multi-domain variable coefficient heat conduction problem with heat source. Both the virtual source function on the virtual boundary and heat source within each subdomain are approximate by the radial basis function interpolation. The equation of the proposed technique is derived by one of the weighted residual methods, namely the Galerkin method, for multi-domain variable coefficient heat conduction problem with heat source. Therefore, VBMGM simultaneously possesses the merits of Galerkin method, boundary element method and meshfree method. And the numerical meanings of the weighted values are definite, such as the partial derivative heat source expressions, the temperature, the heat flux and the continuity conditions, in VBMGM for multi-domain variable coefficient heat conduction problem with heat source. The specific and detailed equation of VBMGM is obtained for multi-domain variable coefficient heat conduction problem with heat source. The accuracy and the stability of the proposed technique are validated by two numerical examples for multi-domain variable coefficient heat conduction problem with heat source. [ABSTRACT FROM AUTHOR]

The virtual boundary meshfree Galerkin method (VBMGM) is presented to calculate the single-domain heat conduction with heat source problem. The virtual source function of the virtual boundary and the heat source in the computational domain both are interpolated by the radial basis function interpolation. The equation of the proposed method is obtained by the Galerkin method of the weighted residual methods. Consequently, VBMGM possesses the advantages of Galerkin method, boundary element method and meshfree method. And the numerical meanings of the weighted values in VBMGM, such as the partial derivative the temperature, the heat flux and the heat source expression, are definite. The detailed and specific equation of VBMGM is deducted. The numerical examples, namely the temperatures of the rectangular domain and the square domain, are computed. And the accuracy and the stability of the proposed method for the single-domain heat conduction with heat source problem are validated. [ABSTRACT FROM AUTHOR]