Reissner-Mindlin shell theory based on tangential differential calculus
Graz University of Technology（格拉茨工业大学）
D. Schöllhammer, T. P. Fries
备注：
Submitted to Computer Methods in Applied Mechanics and Engineering V1: Initial submission. V2: Revised version. arXiv admin note: text overlap with arXiv:1805.11978
The linear Reissner-Mindlin shell theory is reformulated in the frame of the tangential differential calculus (TDC) using a global Cartesian coordinate system. The rotation of the normal vector is modelled with a difference vector approach. The resulting equations are applicable to both explicitly and implicitly defined shells, because the employed surface operators do not necessarily rely on a parametrization. Hence, shell analysis on surfaces implied by level-set functions is enabled, but also the classical case of parametrized surfaces is captured. As a consequence, the proposed TDC-based formulation is more general and may also be used in recent finite element approaches such as the TraceFEM and CutFEM where a parametrization of the middle surface is not required. Herein, the numerical results are obtained by isogeometric analysis using NURBS as trial and test functions for classical and new benchmark tests. In the residual errors, optimal higher-order convergence rates are confirmed when the involved physical fields are sufficiently smooth.
Analysis of hybrid methods of mixed-shear-projected triangular and quadrilateral elements for Reissner-Mindlin plates
School of Mathematics, Southwest Jiaotong University（西南交通大学数学学院）；School of Mathematics, Sichuan University（四川大学数学学院）；Experiment Center, China West Normal University（西华师范大学实验中心）
Robust equilibrated a posteriori error estimators for the Reissner-Mindlin system
Université des Sciences et Technologies de Lille（里尔科学技术大学）；Laboratoire Paul Painlevé UMR 8524（保罗·潘勒韦实验室）；EPI SIMPAF - INRIA Lille Nord Europe（INRIA北欧洲SIMPAF项目组）；Université de Valenciennes et du Hainaut Cambrésis（瓦朗谢讷及康布雷埃斯-哈诺大学）；LAMAV, FR CNRS 2956（拉马夫，法国国家科学研究中心2956）；Institut des Sciences et Techniques de Valenciennes（瓦朗谢讷科学与技术研究所）
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）
Analysis of the Discontinuous Petrov-Galerkin Method with Optimal Test Functions for the Reissner-Mindlin Plate Bending Model
King Abdullah University of Science and Technology (KAUST) Center for Numerical Porous Media（阿卜杜拉国王科技大学多孔数值研究中心）；Aalto University School of Engineering Department of Civil and Structural Engineering（阿尔托大学土木与结构工程学院）
A rotation-based geometrically nonlinear spectral Reissner--Mindlin shell element
Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau（莱茵兰-普法尔茨技术大学凯泽斯劳滕-兰道分校）；Brandenburgische Technische Universität Cottbus-Senftenberg（勃兰登堡科技大学科特布斯-森夫滕贝格分校）
