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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.

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