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

TL;DR

This paper introduces an advanced immersed boundary conformal method (IBCM) for analyzing complex shell structures based on Kirchhoff-Love and Reissner-Mindlin theories, emphasizing boundary conformity, local refinement, and high accuracy.

Contribution

The work develops a novel IBCM framework combining boundary layers, spline approximation, and Nitsche coupling for efficient shell analysis within immersed domains.

Findings

Demonstrates high accuracy in shell simulations

Shows effective boundary condition enforcement

Validates with complex shell examples

Abstract

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.