The isogeometric MITC shell in geometric nonlinear analysis

Abstract

This paper extends the isogeometric MITC shell formulation proposed by Mi and Yu (2021) for linear analysis to address geometric nonlinear shell problems. Built on the Reissner-Mindlin shell theory, the original linear formulation employs the Mixed Interpolation of Tensorial Components (MITC) technique to alleviate shear and membrane locking. The present nonlinear extension retains the MITC framework while incorporating a mixed Non-Uniform Rational B-Spline (NURBS)-Lagrange interpolation strategy to address the additional complexities induced by geometric nonlinearity. The interpolatory nature of the Lagrange basis functions is leveraged to simplify the construction of director vectors and assumed strain fields. The nonlinear problem is formulated in a total Lagrangian setting and solved using Newton-Raphson iterations. The effectiveness of the proposed method is demonstrated through a comprehensive set of numerical examples, including both standard benchmarks and a collection of geometric nonlinear shell problems, which features challenging behaviors such as large rotations and the development of local creases. Through Bézier extraction, the method is further evaluated using T-spline and U-spline basis functions. The numerical results confirm that the MITC technique effectively suppresses shear and membrane locking, and the proposed shell formulation exhibits high accuracy and robust convergence, even for coarse and severely distorted meshes. However, it is also observed that the high inter-element continuity inherent in splines-based discretization can inhibit large deformations, introducing a new form of locking. This issue is successfully mitigated using Bézier extraction to reduce the inter-element continuity. Overall, the proposed formulation offers a general and reliable isogeometric framework for geometrically nonlinear analysis, applicable across a wide range of shell geometries, loading conditions, and boundary constraints.