In the present work, a novel class of hybrid elements is proposed to alleviate the locking anomaly in non-uniform rational B-spline (NURBS)-based isogeometric analysis (IGA) using a two-field Hellinger-Reissner variational principle. The proposed hybrid elements are derived by adopting the independent interpolation schemes for displacement and stress field. The key highlight of the present study is the choice and evaluation of higher-order terms for the stress interpolation function to provide a locking-free solution. Furthermore, the present study demonstrates the efficacy of the proposed elements with the treatment of several two-dimensional linear-elastic benchmark problems alongside the conventional single-field IGA, Lagrangian-based finite element analysis (FEA), and hybrid FEA formulation. It is shown that the proposed class of hybrid elements performs effectively for analyzing the nearly incompressible problem domains that are severely affected by volumetric locking along with the thin plate and shell problems where the shear and membrane locking is dominant. A better coarse mesh accuracy of the proposed method in comparison with the conventional formulation is demonstrated through various numerical examples. Moreover, the formulation is not restricted to the locking-dominated problem domains but can also be implemented to solve the problems of general form without any special treatment. Thus, the proposed method is robust, most efficient, and highly effective against different types of locking.
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）
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）
