A universal parameterized absolute nodal coordinate formulation for arbitrarily shaped shells

Absolute node coordinate formulation (ANCF) has been widely applied to the large deformation and nonlinear dynamic problems of plate/shell structures. Nevertheless, the complex geometries of plate/shell structures and the higher-order discontinuity of gradients have hindered the widespread engineering application of higher-order ANCF elements. In this work, a parameterized ANCF approach tailored for plate/shell structures with complex geometries and multi-connected features is developed, providing a new solution for nonlinear dynamic simulation of complex plate/shell structures in engineering applications. The boundary first flattening (BFF) is used to map complex plate/shell structures onto specified planar domains and achieve global parameterization. Within the parameterized plane, the B-spline interpolation techniques are utilized to construct higher-order gradient vectors for such structures. Finally, various higher-order ANCF elements are applied within the parameterized plane to accurately simulate the nonlinear dynamics of complex plate/shell structures. The proposed method effectively solves the problem of higher-order gradient discontinuity, enabling the application of higher-order ANCF elements to the nonlinear dynamics of plate/shell structures with complex geometries and multi-connected features, thereby expanding ANCF's application scope. On the other hand, the global parameterization of plate/shell structures and higher-order gradient construction are computed only once prior to simulation, which features low offline costs and introduces no additional computational overhead for static/dynamic simulations. Furthermore, owing to its enhanced continuity and utilization of higher-order ANCF elements, this method ensures computational accuracy with fewer mesh elements, reducing computational costs while improving efficiency. The efficacy and reliability of the proposed method are verified by modal frequency comparison, static equilibrium and dynamic response.