Optimization of material composition of functionally graded plate for thermal stress relaxation using a genetic algorithm

In this article, a genetic algorithm is applied to an optimization problem of material composition for a plate of step-formed functionally graded materials The step-formed functionally graded plate is analyzed as a laminated composite plate made of numerous layers with homogeneous and different isotropic material properties. First the one-dimensional transient temperature distribution for a laminated plate is analyzed theoretically. In addition, the thermal stress components for such an infinitely long plate are formulated under the mechanical condition of being traction-free. As a numerical example, a plate composed of zirconium oxide and titanium alloy is considered. In addition, for the optimization problem of minimizing the thermal stress distribution, the numerical calculations are made using a genetic algorithm without supposing a distribution function of material composition and the optimal material composition of each layer is determined taking into account the effect of the temperature dependency of material properties. Furthermore, the results obtained when a distribution function isn't specified and the results found when a distribution function is specified are compared.