  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.
