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On the accuracy of Reissner-Mindlin plate model for stress boundary conditions. (English) Zbl 1137.74397
For a plate subject to stress boundary condition, the deformation determined by the Reissner-Mindlin plate bending model could be bending dominated, transverse shear dominated, or neither (intermediate), depending on the load. We show that the Reissner-Mindlin model has a wider range of applicability than the Kirchhoff-Love model, but it does not always converge to the elasticity theory. In the case of bending domination, both the two models are accurate. In the case of transverse shear domination, the Reissner-Mindlin model is accurate but the Kirchhoff-Love model totally fails. In the intermediate case, while the Kirchhoff-Love model fails, the Reissner-Mindlin solution also has a relative error comparing to the elasticity solution, which does not decrease when the plate thickness tends to zero. We also show that under the conventional definition of the resultant loading functional, the well known shear correction factor 5/6 in the Reissner-Mindlin model should be replaced by 1. Otherwise, the range of applicability of the Reissner-Mindlin model is not wider than that of Kirchhoff-Love’s.

##### MSC:
 74K20 Plates 74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics 74C99 Plastic materials, materials of stress-rate and internal-variable type
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