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On the mathematical foundation of the $$(1,1,2)$$-plate model. (English) Zbl 0962.74036
This paper considers the plate problem in three-dimensional linear elastostatics in the framework of hierarchical modelling with the help of the energy projection method. In particular, the so-called $$(1,1,2)$$-bending model is discussed with emphasis on the applicability of unmodified three-dimensional material laws. It is shown that in some sense the $$(1,1,2)$$-bending model is the simplest asymptotically correct model in the hierarchical family. The authors present error estimates for the deviation of the $$(1,1,2)$$-solution from the Kirchhoff solution as well as from the three-dimensional solution. The results are illustrated by a numerical example.

##### MSC:
 74K20 Plates 74B05 Classical linear elasticity 74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
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