  This work utilizes the Immersed Boundary Conformal Method (IBCM) to analyze
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 the simplicity of the approach. The IBCM
method introduces additional layers conformal to the 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 the 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 of Kirchhoff-Love and
Reissner-Mindlin theories, and the simulation of a damaged shell.
