Analysis of shear locking in Timoshenko beam elements using the function space approach13; 13;

Elements based purely on completeness and continuity requirements perform erroneously in a certain class of problems. These are called the locking situations, and a variety of phenomena like shear locking, membrane locking, volumetric locking etc. has been identified. Locking has been eliminated by many techniques, e.g. reduced integration, addition of bubble functions, use of assumed strain approaches, mixed and hybrid approaches, etc.. The field-consistency paradigm offers a priori error estimates for locking phenomena, and provides procedures to define field consistent, assumed strains which free the element from locking. In this paper, the field consistency paradigm is reviewed using a function space model, and a method is proposed to identify field-inconsistent spaces for projections that show locking behavior. The case of the Timoshenko beam serves as an illustrative exampl