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Unlocking with residual-free bubbles. (English) Zbl 0890.73064
Summary: Residual-free bubbles are derived for the Timoshenko beam problem. After eliminating these bubbles, the resulting formulation is form-identical in using the following tricks to the standard variational formulation: (i) one-point reduced integration of the shear energy term; (ii) replace its coefficient \(1/ \varepsilon^2\) by \(1/ (\varepsilon^2 + (h^2_K /12))\) in each element; (iii) modify consistently the right-hand side. This final formulation is ‘legally’ obtained in that the Galerkin method enriched with residual-free bubbles is developed using full integration throughout. Furthermore, this method is nodally exact by construction.

74S05 Finite element methods applied to problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
Full Text: DOI
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