Analysis of shear locking in Timoshenko beam elements using the function space approach

Abstract

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., have 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. In this paper, we review the field consistency paradigm using a function space model, and propose a method to identify field-inconsistent spaces for projections that show locking behaviour. The case of the Timoshenko beam serves as an illustrative example.