Thermomechanical analysis of functionally graded materials using the Galerkin method

Functionally graded materials or FGMs are characterized by a material construction containing no distinct material phases. This construction results in continuously or near continuously varying material properties. Analysis and design of FGMs present a challenging computational problem. Existing methods of analysis developed for composite materials do not necessarily work well for FGMs. These methods assume the material phases are distinct which is not the case with FGMs. A semi-analytical approach is introduced to obtain steady-state thermal stress fields in FGMs. The governing equations for both steady-state heat transfer and elastic equilibrium are solved using the Galerkin type trial functions that satisfy the given homogeneous boundary conditions, and the coefficients of the trial functions are determined using the Galerkin method. Thermomechanical analysis using the Galerkin method is developed and applied to a non-specific functionally graded material. The method is implemented utilizing a computer algebra system.