A study of stabilization and projection in the 4-node Mindlin plate element. (English) Zbl 0717.73068
Summary: A Mindlin plate element is formulated based on the Hellinger-Reissner principle and the \(\gamma\)-technique. The stiffness consists of a constant stress matrix (one-point quadrature) and a stabilization matrix. The stabilization matrix is compared with those previously proposed [the second author and Ch.-Sh. Tsay, ibid. 19, 405-419 (1983; Zbl 0502.73058)]. In addition, the element uses a projection to modify the nodal displacements so that the patch test is satisfied. The projection matrix is based on a mode decomposition. Several numerical cases are presented, and it is shown that the mode decomposition projection is necessary both for satisfaction of the patch test and convergence.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74K20 | Plates |
| 49M27 | Decomposition methods |
| 74S30 | Other numerical methods in solid mechanics (MSC2010) |
| 74P10 | Optimization of other properties in solid mechanics |
Keywords:
gamma technique; Hellinger-Reissner principle; constant stress matrix (one-point quadrature); stabilization matrix; projection matrix; mode decompositionCitations:
Zbl 0502.73058References:
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