A micromechanical approach is adopted to systematically obtain numerical Green’s function for functionally graded materials (FGMs) which enables expressing thermomechanical fields in FGMs as a convolution type of integrals between the Green’s function and a source function. The numerical Green’s function is sought by the eigenfunction expansion method. Computer algebra systems are essential to derive admissible functions that satisfy the given boundary conditions and manipulation of the algebra involved. Using the Green’s function for FGMs, physical fields in FGMs can be expressed semi-analytically while retaining all the relevant parameters. In addition, any change in boundary conditions such as temperature can be readily reflected without incurring the entire recalculation.

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