A Physics Informed Neural Network Framework for Optimization of Functionally Graded Materials for Aerostructural Systems

Optimizing functionally graded materials (FGMs) is critical for aerospace structures, where adjusted material distributions can enhance performance under complex loading, boosting structural instability margins, reducing weight, and mitigating stress concentrations. This study presents a data‑free, partial differential equation (PDE)‑driven framework that uses physics‑informed neural networks (PINNs) as high‑fidelity surrogates for FGM design in beams and plates. Spatial gradation is captured by a compact vector of design variables, where FGM profile will be enforced solely through its governing PDE residuals in addition to boundary and initial conditions. Trained with minimum measurement or simulation data, the model learns the coupled physics from first principles. A nested optimization loop, identifies optimal gradation profiles that minimizes total deflection. Demonstrated on a cantilever beam in free vibration, the approach matches the accuracy of finite element simulations. The framework is applied to the free vibration of a functionally graded plate, after which the PINN surrogate is used to perform the deflection-minimization optimization. The optimal design obtained from the PINN model is consistent with the FEM-based solution, confirming the accuracy of the surrogate. Future extensions will incorporate additional loading cases, plate geometries, enabling integration of FGM co‑design for demanding aerospace applications.