Communications in Numerical Methods in Engineering · 2001 · 36 citations · 4 references
EngineeringComputational EngineeringMechanical EngineeringComputational MechanicsFinite Element AnalysisFinite Element MethodsBeam AnalysisBeam TheoryBending Of BeamsStress AnalysisStructural Finite Element AnalysisVibration AnalysisBeam ElementsBeam Finite Element AnalysisContinuity RequirementsLockingLocking PhenomenaMembrane LockingShear LockingTimoshenko Beam Theory
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. Copyright © 2001 John Wiley & Sons, Ltd.
4