On boundary layer in the Mindlin plate model: Levy plates

Abstract

This work is related to the bending problem of thick rectangular Levy plates. Series solution for the Mindlin (thick) plate model is obtained and represented as a sum of the Kirchhoff (thin) plate model solution, the “shear terms” and the “boundary layer terms”. Hard- and soft-simple supported, hard- and soft-clamped and free boundary conditions are considered. In order to detect plate regions where Kirchhoff model is good enough, and plate regions where Mindlin model should be used, a model error indicator is introduced. Several examples are presented, illustrating the difference between the Mindlin and the Kirchhoff results, the strengths of boundary layers for different boundary conditions, accuracy of several possible model error indicators and dependence of results on plate thickness.