Mukherjee, Somenath; Prathap, Gangan Analysis of shear locking in Timoshenko beam elements using the function space approach. (English) Zbl 1052.74587 Commun. Numer. Methods Eng. 17, No. 6, 385-393 (2001). 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. Cited in 9 Documents 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 Keywords:field-consistency; projection theorem PDFBibTeX XMLCite \textit{S. Mukherjee} and \textit{G. Prathap}, Commun. Numer. Methods Eng. 17, No. 6, 385--393 (2001; Zbl 1052.74587) Full Text: DOI References: [1] Zienkiewicz, The Finite Element Method (1991) [2] Tessler, An improved treatment of transverse shear in the Mindlin type four node quadrilateral element, Computational Methods in Applied Mechanics and Engineering 39 pp 311– (1983) · Zbl 0501.73072 · doi:10.1016/0045-7825(83)90096-8 [3] Carpenter, Locking and shear scaling factors in C0 bending elements, Computers and Structures 22 pp 39– (1986) · Zbl 0573.73086 · doi:10.1016/0045-7949(86)90083-0 [4] Prathap, Field-consistency and violent stress oscillations in the finite element method, International Journal for Numerical Methods in Engineering 24 pp 2017– (1987) · Zbl 0622.73076 · doi:10.1002/nme.1620241013 [5] Prathap, Reduced integration and the shear flexible beam element, International Journal for Numerical Methods in Engineering 18 pp 195– (1982) · Zbl 0473.73084 · doi:10.1002/nme.1620180205 [6] Edwards, Elementary Linear Algebra (1988) · Zbl 0713.15001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.