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.
The performance of the DK (Discrete Kirchhoff) and DKM (Discrete Kirchhoff-Mindlin) shell element classes in the upper bound finite-element-based limit analysis and in the sequential finite-element-based limit analysis
Analytical properties of polygonal Stokes and BGG Hessian complexes with application to Kirchhoff--Love plates
IMAG, Univ. Montpellier, CNRS（蒙彼利埃大学，法国国家科学研究中心）；School of Mathematics, Monash University（莫纳什大学数学学院）；Mathematical Institute, University of Oxford（牛津大学数学研究所）
A new locking-free polygonal plate element for thin and thick plates based on Reissner-Mindlin plate theory and assumed shear strain fields
University of Chile（智利大学）；Indian Institute of Technology-Madras（印度理工学院马德拉斯分校）；University of Luxembourg（卢森堡大学）；Cardiff University（卡迪夫大学）；Duy Tan University（Duy Tan 大学）
A General-Purpose, Inelastic, Rotation-Free Kirchhoff-Love Shell Formulation for Peridynamics
我们提出了一个全面的无旋转Kirchhoff-Love（KL）壳的周波（PD），能够模拟大的弹塑性变形和薄壁结构的断裂制定。为了消除对预定义的全局参数域的需要，在无网格设置中采用主成分分析来开发壳中间曲面的局部参数化。KL壳运动学被用来开发一个基于对应的PD制定。一个键稳定技术自然实现离散解的稳定性。在控制薄壳方程中只使用了中表面速度自由度。采用3D速率形式的材料模型来模拟各种材料行为。采用键关联损伤对应建模方法，在键级使用经典的失效准则，这很容易使模拟的脆性和韧性断裂。\NAT{Discretizing the model with asymptotically compatible meshfree approximation provides a scheme which converges to the classical KL shell model while providing an accurate and flexible framework for treating fracture.}一个广泛的数值例子，从弹性静力学的问题，涉及塑性，断裂和破碎，进行验证的准确性，收敛性和鲁棒性的PD薄壳制定。还值得注意的是，本方法自然地使得能够在完全非结构化的表面网格上离散化需要高阶光滑度的壳理论。
A natural framework for isogeometric fluid-structure interaction based on BEM-shell coupling
SISSA-International School for Advanced Studies（国际高等研究院）；Technische Universität Braunschweig（布伦瑞克工业大学）；University of Pavia（帕维亚大学）；Technische Universität München（慕尼黑工业大学）
