Penalty methods have proven to be particularly effective for achieving the required $C^1$-continuity in the context of multi-patch isogeometric Kirchhoff-Love shells. Due to their conceptual simplicity, these algorithms are readily applicable to the displacement and rotational coupling of trimmed, non-conforming surfaces. However, the accuracy of the resulting solution depends heavily on the choice of penalty parameters. Furthermore, the selection of these coefficients is generally problem-dependent and is based on a heuristic approach. Moreover, developing a penalty-like procedure that avoids interface locking while retaining optimal accuracy is still an open question. This work focuses on these challenges. In particular, we devise a penalty-like strategy based on the $L^2$-projection of displacement and rotational coupling terms onto a degree-reduced spline space defined on the corresponding interface. Additionally, the penalty factors are completely defined by the problem setup and are constructed to ensure optimality of the method. To demonstrate this, we asses the performance of the proposed numerical framework on a series of non-trimmed and trimmed multi-patch benchmarks discretized by non-conforming meshes. We systematically observe a significant gain of accuracy per degree-of-freedom and no interface locking phenomena compared to other penalty-like approaches. Lastly, we perform a static shell analysis of a complex engineering structure, namely the blade of a wind turbine.
Unveiling the Multiphysics Complexity: An Isogeometric Framework for Inducing Bifurcation and Tracing Post-Buckling Paths in Electroelastic Thin Shells
College of Mechanics and Engineering Science, Hohai University（河海大学力学与工程科学学院）；Glasgow Computational Engineering Centre, James Watt School of Engineering, University of Glasgow（格拉斯哥大学詹姆斯瓦特工程学院格拉斯哥计算工程中心）；School of Engineering, Newcastle University（纽卡斯尔大学工程学院）；Institute of Applied Mechanics, Friedrich-Alexander Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希·亚历山大大学应用力学研究所）
Robust approximation error estimates for analysis-suitable $G^1$ isogeometric multi-patch discretizations
Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences（奥地利科学院约翰·拉登计算与应用数学研究所）；Johannes Kepler University（约翰内斯·开普勒大学）
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）
