Bending Solutions of Sectorial Mindlin Plates from Kirchhoff Plates

Abstract

This study presents exact relationships between the bending solutions of sectorial plates based on the Kirchhoff (or classical thin) plate theory and the Mindlin plate theory. While the former plate theory neglects the effect of transverse shear deformation, the latter theory allows for this effect, which becomes significant when dealing with thick plates and sandwich plates. The considered sectorial plates have simply supported radial edges, while the circular curved edge may be either simply supported, or clamped or free. The availability of such relationships allow easy conversion of the existing Kirchhoff sectorial plate solutions into the corresponding Mindlin solutions, thus bypassing the need to solve the more complicated bending equations of the Mindlin plates. The use of the relationships is illustrated using some sectorial plate examples, and sample solutions obtained were checked with previous researchers' results and those computed from the software ABAQUS.