Multi-objective Optimization of Stiffening Rings in Spherical Sandwich Shells for Enhanced Free Vibration Performance

This study introduces a refined multi-objective optimization framework using the Non-dominated Sorting Genetic Algorithm II (NSGA-II). It strategically positions solid stiffening rings in spherical sandwich shells to enhance a defined set of natural frequencies. The NSGA-II employs fast non-dominated sorting, crowding distance assignment, and elitist selection to maintain solution diversity and convergence. This method efficiently explores the design space, balancing conflicting objectives to produce a well-distributed Pareto front. Optimized configurations offer potential for aerospace applications, including lightweight satellite structures and high-performance pressure vessels that demand superior modal characteristics. The sandwich shells consist of graphene platelet-reinforced nanocomposite (GPLRC) face sheets and a porous core. The model is based on first-order shear deformation theory (FSDT) and Sanders’ strain relations for deep shells, with linear elasticity for each layer. Stiffening rings are modeled as artificial circumferential springs. The 2D Ritz method with a combination of Chebyshev and trigonometric polynomials minimizes the system’s Lagrangian to derive the governing equations. Solving the eigenvalue problem provides the natural frequencies. This NSGA-II-based approach delivers a robust Pareto front of optimal ring placements, advancing frequency-based optimization in spherical sandwich shell structures. Results demonstrate that the optimized configurations achieve significant frequency enhancement, confirming the effectiveness of the proposed approach in structural vibration control.