Extraction of Mindlin plates’ shear correction factors from Reddy plate theory

Abstract

Although consisting of more simplifying assumptions than the Reddy plate theory, the Mindlin plate theory is nevertheless attractive in accounting for shear deformation due to its convenience in execution. Notwithstanding its simplicity, the highly accurate Mindlin plate solution is achievable by judicious choice of shear correction factor. This paper describes generalised methods for extracting the exact shear correction factor for a class of simply supported Mindlin plates within the framework of Reddy plate theory. Based on the matching of transverse deflection of polygonal plates as well as the buckling load of polygonal and circular plates between Mindlin and Reddy plates, results reveal that the constant shear correction factor of 14/17 is the least accurate while 5/6 is the better lower bound, and that a slight modification to the exact shear correction factor gives a tight upper bound. The exact shear correction factor obtained herein allows the Mindlin plate solution to be exactly equal to the Reddy plate, while the tight bounds are useful for precision design purposes.