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Analysis of shear locking in Timoshenko beam elements using the function space approach. (English) Zbl 1052.74587

Summary: 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 Timoshenko beam serves as an illustrative example.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
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References:

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