Boundary Layer Phenomenon in the Limit Analysis of Reissner- Mindlin Plates

Resumo

The Kirchhoff and Reissner-Mindlin plate theories are the most frequently used models for describing
the behavior of linearly elastic plates. In what concern the limit analysis of plates based on the static theorem, the
most significant difference between those theories lies in the fact that for a Reissner-Mindlin plate the transverse
shear resistance is included in the yield criterion. It is numerically shown that the Kirchhoff plate theory
increasingly overpredicts the collapse load of plates with decreasing side-to-thickness ratio. For this reason alone,
the Reissner-Mindlin plate theory should be used in the limit analysis of relatively thick plates. On the other hand,
transverse shear locking and boundary layer have been major sources of convergence delay of Reissner-Mindlin
plate models, especially towards thin plate solutions. While the former is a well investigated finite element defect,

the latter is a real physical phenomenon likely to be manifested in more refined theories, such as the Reissner-
Mindlin plate theory, that nearly no attention has been paid in the framework of yield design. In this sense, it is

used in the present work a recently developed shear locking-free finite element for the yield design of Reissner-
Mindlin plates based on the static theorem to illustrate boundary layers along certain types of plate edges, which

may not be of the same type as those in linear elastic solutions. Finally, a brief state-of-the-art review about limit
analysis of Reissner-Mindlin plates is then provided.