A mixed finite element formulation for Reissner-Mindlin plates based on the use of bubble functions. (English) Zbl 0717.73069
Summary: A new finite element formulation for Reissner-Mindlin plates, based on the Hellinger-Reissner variational principle, is proposed in which the displacement field is additively decomposed into two parts: a part associated with standard interpolation of nodal degrees of freedom and a part associated with a set of independent bubble functions expressed in terms of generalized parameters. The formulation employs independent approximations for every stress component so that the stress field does not a priori satisfies the homogeneous equilibrium equations. It is shown that the bubble functions provide additional variational constraints on the stress field, resulting in optimal accuracy for the mixed formulation, and also eliminating shear locking in the thin limit. A 4- node and a 9-node element are described in detail. Both elements pass the patch test for mixed elements described by O. C. Zienkiewicz, S. Qu, R. L. Taylor and S. Nakazawa [ibid. 23, 1873-1883 (1986; Zbl 0614.65115)] and are stable in the sense of the Babuška- Brezzi condition. Numerical results indicate that the elements are accurate in displacements and stresses, including transverse shear, and insensitive to mesh distortion.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74K20 | Plates |
| 74S30 | Other numerical methods in solid mechanics (MSC2010) |
| 74P10 | Optimization of other properties in solid mechanics |
Keywords:
Hellinger-Reissner variational principle; displacement field; decomposed into two parts; standard interpolation of nodal degrees of freedom; set of independent bubble functions; generalized parameters; independent approximations for every stress component; variational constraints; 4- node; 9-node element; patch test for mixed elements; Babuška-Brezzi conditionCitations:
Zbl 0614.65115References:
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