A modal-based shape optimization methodology for conventionally shaped patches in composite plate repair

Composite materials are known to excel in high-performance applications, particularly in the aerospace industry. Due to this fact, there is a growing concern regarding the maintenance, repair, and overhaul operations of such materials. Within this context, the best approaches for restoring the degraded mechanical properties of composites converge towards the use of fiber-reinforced adhesive patches. The present work proposes a novel methodology for the shape optimization of patches for the recovery of locally damaged composite plates. A shape optimization problem was formulated with the aim of minimizing the error associated with the modal response of the repaired structure to that of the undamaged one. Sequential linear programming was employed alongside an interior point algorithm to attain the optimized dimensions of rectangular single-sided patches, which were used in the restoration of simply supported damaged square panels. The damage was introduced by the mechanical removal of material along the central region. Modal and three-point bending tests were conducted to evaluate the performance of the patch repair. The modal response of the repaired panels indicated an efficiency of 98.2% restoration of the first natural frequency. The effectiveness in terms of mechanical strength was 94.0% in restoring the maximum resisted load, and 96.5% in terms of the ultimate displacement.