Abstract
Robust solution procedures remain a significant challenge in the finite element analysis of slender shell structures undergoing large deformations. Classical Newton-Raphson methods often require small load increments and initial guesses close to equilibrium to achieve convergence. In this work, we formulate a geometrically exact shell model with drilling rotations as an energy minimization problem on a configuration manifold. Within this framework, the corresponding Riemannian gradient and Hessian are derived and used to construct a Riemannian trust-region method for nonlinear shell analysis. The proposed method acts as a globalization strategy and is capable of converging from configurations far from equilibrium. Its performance is evaluated on several benchmark problems involving large deformations and buckling, as well as on an industrial flat-cable application. The results demonstrate that the proposed method consistently converges in cases where conventional Newton-Raphson methods fail, thereby providing a robust solution strategy for geometrically nonlinear shell problems.