High-performance multi-layered Functionally Graded Materials (FGMs) have a wide range of structural applications, such as modern engine and turbine technologies. However, in most technical applications the difference between the FGM layers' thermal expansion coefficients and Young's moduli induces stress and strain fields during operation. These stresses and strains can result in failure of the FGM if, for example, the tensile strength of a brittle partner is exceeded. In optimizing composite structures with respect to material compatibility, the objective is to achieve an FGM design which minimizes failure stresses in the layers. High-performance composites of this kind permit a wide variety of applications beyond the range of the individual materials. For the design of FGMs under thermo-mechanical loads, a simulation model on the basis of analytical solutions is presented. This model allows - in contrast to the Finite Element Method - a quick and efficient variation of material parameters, such as the thermal expansion coefficient and Young's modulus, as well as the optimization of thickness ratios. For the example of a thermo-mechanically loaded FGM plate, a variation of material and geometrical parameters is performed.