A mesh re-parameterization method using bilinear Möbius transformation for static, free vibration and buckling analyses of shells

Accurate analysis of shell structures is challenging due to their geometric complexity, mesh sensitivity and mechanical prediction reliability. To address this challenge, this work presents a mesh re-parameterization method for isogeometric analysis of shells using the bilinear Möbius transformation. Based on the Reissner-Mindlin theory, Non-Uniform Rational B-splines (NURBS) basis functions are employed as shape functions to accurately represent the shell geometry. Re-parameterization of the NURBS surface is achieved using the bilinear Möbius transformation, which introduces free parameters and applies linear interpolation to the basis functions. The values of the free parameters are determined by employing the Grey Wolf Optimizer algorithm. To evaluate the mesh quality before and after the bilinear Möbius transformation, the mesh shape quality coefficient is further constructed as the evaluation criterion. The re-parameterized NURBS basis functions are then used to discretize the shell structures, thereby enabling accurate isogeometric analysis. Finally, the present method is validated by examples of a free-form shell with large curvature, a simplified turbine blade and a square plate with a circular hole. The results demonstrate the present method possesses the following important advantages: (1) higher accuracy; (2) stronger adaptability; (3) faster convergence rate; (4) good stability.