Reliability-based design optimization of volume fraction distribution in functionally graded composites

Functionally graded material (FGM) has a continuous and functional distribution of volume fractions of constituent particles, which leads to superior thermo-mechanical performance to classical laminated composite materials. Since the thermo-mechanical characteristics of an FGM depend on the volume fraction distribution, it is important to tailor appropriate volume fraction distribution that satisfies the desired performance requirements under given loading and boundary conditions. Even though numerical optimization technique may serve as an excellent material tailoring tool, the capacity of current manufacturing techniques of FGM may not yield the target volume fraction. To deal with uncertainty in the manufacturing process, a reliability-based design optimization (RBDO) for FGM composite is proposed. In RBDO, a finite number of volume fractions of homogenized FGM layers and material properties are considered as random variables, with statistical information such as mean, standard deviation, and statistical distributions. Design of experiments and response surface models are used to obtain explicit forms of thermal stresses for RBDO formulation. It is observed through the numerical experiment that the RBDO finds the optimized volume fraction distribution with high reliability, such that the graded layers do not fail in the presence of manufacturing uncertainty.