CVEM coupled with Newton iteration for geometrically nonlinear generalized membrane shell model

Existing shell theories and models are predominantly based on the assumptions of small strain and linear elasticity. However, when the structure undergoes large displacements or rotations under loading, geometric nonlinearities become non-negligible, necessitating a nonlinear theory to accurately characterize its mechanical behavior. In this work, a conforming virtual element method (CVEM) is proposed for nonlinear shell problems. The Newton iteration method is employed to linearize the geometric nonlinear terms in the model, thereby constructing a linearized discrete formulation for the two-dimensional nonlinear generalized membrane shell model. Moreover, the unique solvability of the discrete system is proved using Brouwer’s fixed-point theorem. Finally, numerical experiments on typical generalized membrane shell examples demonstrate that the nonlinear model effectively overcomes the distortion inherent in linear models when describing finite deformations. The onstructed virtual element discretization exhibits excellent numerical stability, convergence, and adaptability to complex meshes.