Utilization of a Linear Solver for Multiscale Design and Optimization of Microstructures

Microstructures have a significant effect on the performance of critical components in numerous aerospace metallic material applications. Examples include panels in airframes that are exposed to high temperatures and sensors used for vibration tuning. This paper addresses the techniques to optimize the microstructure design for polycrystalline metals. The microstructure is quantified with the orientation distribution function that determines the volume densities of crystals that make up the polycrystal microstructure. The orientation distribution function of polycrystalline alloys (e.g., hexagonal close-packed titanium) is represented in a discrete form, and the volume-averaged properties are computed through the orientation distribution function. The optimization is performed using the space of all possible volume-averaged macroproperties (stiffness and thermal expansion). A direct linear solver is employed to find the optimal orientation distribution functions. The direct solver is capable of finding exact solutions even for problems with multiple or infinite solutions. It is first applied to the optimization of the panel-buckling problem. The objective of the buckling optimization problem is to find the best microstructure design that maximizes the critical buckling temperature. The optimum solution computed with this approach is found to be same as the optimum solution of a global approach that uses a genetic algorithm. The linear solver methodology is extended to plastic properties and applied to explore the design of a Galfenol beam microstructure for vibration tuning with a yielding objective. The design approach is shown to lead to multiple optimum solutions.