The Immersed Boundary Conformal Method for Kirchhoff–Love and Reissner–Mindlin shells

This work utilizes the Immersed Boundary Conformal Method (IBCM) to analyze linear elastic Kirchhoff-Love and Reissner-Mindlin shell structures within an immersed domain framework. Immersed boundary methods involve embedding complex geometries within a background grid, which allows for great flexibility in modeling intricate shapes and features despite simplicity of the approach. The IBCM method introduces additional layers conformal to boundaries, allowing for the strong imposition of Dirichlet boundary conditions and facilitating local refinement. In this study, the construction of boundary layers is combined with high degree spline-based approximation spaces to further increase efficiency. The Nitsche method, employing non-symmetric average operators, is used to couple the boundary layers with inner patch, while stabilizing the formulation with minimal penalty parameters. High-order quadrature rules are applied for integration over cut elements and patch interfaces. Numerical experiments demonstrate the efficiency and accuracy of the proposed formulation, highlighting its potential for complex shell structures modeled through Kirchhoff-Love and Reissner- Mindlin theories. These tests include the generation of conformal interfaces, the coupling Kirchhoff-Love and Reissner-Mindlin theories, and the simulation of a cylindrical shell with through-the-thickness crack.