Geometric Nonlinear Analysis of Shell Structures: Examine the theoretical framework for conducting geometrically nonlinear analysis of shell structures in civil engineering. Discuss the challenges posed by large deformations and geometric imperfections, and how they influence the structural response of shells under static and dynamic loads. Explore mathematical formulations, such as the Donnell$-$Mushtari$-$Vlasov theory and finite element discretization techniques, used to capture geometric nonlinearity in shell structures accurately. Assess the significance of geometric nonlinear analysis in optimizing the design and performance of shell$-$based systems, including shells used in roofs, domes, and storage tanks, for ensuring structural safety and serviceability.