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

Elements based purely on completeness and continuity requirements perform e rroneously in a certain class of problems. These are called the locking sit uations, and a variety of phenomena like shear locking, membrane locking, v olumetric 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 thi s paper, we review the field consistency paradigm using a function space mo del, and propose a method to identify field-inconsistent spaces for project ions that show locking behaviour. The case of the Timoshenko beam serves as an illustrative example. Copyright (C) 2001 John Wiley & Sons, Ltd.