Effect of geometric imperfections on stability and optimal design of shallow space structures

Shallow space structures such as domes and roof trusses are widely used in large-span engineering due to their high structural efficiency. However, these systems are highly sensitive to geometric imperfections, which can significantly reduce their load-carrying capacity and trigger snap-through instability. In current engineering practice, structural design is often based on linear analysis or nonlinear analysis assuming perfect geometry, which may lead to unsafe and non-conservative results. This study investigates the influence of initial geometric imperfections on the stability and optimal design of shallow space structures. A geometrically nonlinear analysis is performed using a mixed finite element formulation capable of accurately tracing the equilibrium path. A 24-bar star dome is adopted as a benchmark structure, and three design scenarios are considered: linear analysis, nonlinear analysis with perfect geometry, and nonlinear analysis including geometric imperfections. The results reveal that linear and perfect nonlinear designs yield identical optimal solutions, masking critical stability issues. When moderate imperfections are considered, the optimal structural weight increases by approximately 17%, and can rise dramatically for larger imperfections. These findings highlight the necessity of incorporating geometric imperfections in structural analysis and design to ensure safety and reliability.