G. T. Lim

Thick Lévy plates re-visited

Abstract This paper is concerned with the bending problem of Levy plates which are simply supported on two opposite edges with any combination of simply supported, clamped or free conditions at the remaining two edges. This study attempts to solve thick Levy plate problems in a novel way by establishing bending relationships that allow the prediction of Mindlin plate results using the corresponding Kirchhoff solutions. Based on the concept of load equivalence, these relationships obviate the need for complicated thick plate analyses that involve significant computation time and effort. Numerical plate solutions are then determined from these relationships and the validity of these results is verified using other known results and those generated using the abaqus software. It is through this study that the only analytical Mindlin plate solutions by Cooke and Levinson (Int. J. Mech. Sci. 25 (1983) 207) are found to contain errors. In this study, it is found that there are important distinctions between the Mindlin and Reissner plate theories. These differences will also be substantiated by numerical comparison.

Bending of annular sectorial Mindlin plates using Kirchhoff results

This study is concerned with the elastic bending problem of a class of annular sectorial plates whose radial edges are simply supported. Exact bending relationships between the Mindlin plate results and the corresponding Kirchhoff plate solutions have been derived based on the concept of load equivalence. These bending relationships facilitate the deduction of thick (Mindlin) plate results from the corresponding classical thin (Kirchhoff) plate solutions, thus bypassing the need to solve the more complicated governing equations of thick plates. The correctness of the relationships is established by solving the bending problem of annular sectorial plates under a uniformly distributed load and comparing the results with existing thick plate solutions.