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Virtual boundary element-free Galerkin method for nonlinear temperature-dependent variable coefficient thermal transfer in FGMs
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DOI：10.1016/j.enganabound.2026.106837.png)
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Abstract
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High temperature resistant engine components, spacecraft thermal protection systems, functionally graded coatings, and building insulation can withstand extremely high temperature gradients while maintaining structural safety, and reliability. Nonlinear temperature-dependent variable coefficient thermal transfer in functionally graded materials (FGMs) is computed by virtual boundary element-free Galerkin method (VBEGM). This method incorporates the beneficial characteristics of boundary element method, element-free method, and Galerkin method. Kirchhoff's transformations of power-type and exponential-type temperature-dependent thermal conductivity coefficients are introduced. Kirchhoff's transformation of quadratic-type one is derived in detail. The solution is divided into the homogeneous solution and the special solution. Homogeneous solution can be obtained by virtual BEM, which can avoid the singular integral and corner problems. Virtual source function is interpolated by the moving Kriging interpolation, which possesses the attribute of the Kronecker delta. Special solution can be expressed using interpolation of the specialized solution function. The element-free method, which does not require the background mesh, is a true meshfree method and applied to the discretization of homogeneous solution and special solution. Five numerical examples, including quadratic-type, power-type, and exponential-type of temperature-dependent thermal conductivity, are computed and compared with other numerical methods. The validity and correctness of the suggested method have been validated for nonlinear temperature-dependent variable coefficient heat transfer in FGMs.
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