A review of topology optimization methods for the design of shellular structures

Shell structures are renowned for their unparalleled stiffness-to-weight performance through their elegant curvature and material efficiency. This review provides a comprehensive synthesis of the foundational principles and emerging technologies driving the next generation of shell design. It begins by examining key geometric concepts such as minimal surfaces, funicular geometry and inverse design, which enable structurally efficient shapes with minimal material use. The discussion then moves to computational optimization strategies (including size, shape, and topology optimization) as well as data-driven and AI-assisted frameworks that accelerate design exploration and performance prediction. Reinforcement approaches are surveyed next, spanning conventional stiffeners and sandwich shells. These strategies are contextualized through applications in civil infrastructure, aerospace components, and biomedical implants. The review concludes by identifying key challenges such as imperfection sensitivity, fabrication constraints, and multi-objective trade-offs, while highlighting promising directions in hybrid multiscale modeling and sustainable shell design. Together, the topics covered provide an integrated roadmap for the development of intelligent, adaptive, and high-performance shell systems.