Equilibrium approach in the derivation of differential equations for homogeneous isotropic mindlin plates

Abstract

In this paper, the differential equations of Mindlin plates are derived from basic principles by simultaneous satisfaction of the differential equations of equilibrium, the stress-strain laws and the strain-displacement relations for isotropic, homogenous linear elastic materials. Equilibrium method was adopted in the derivation. The Mindlin plate equation was obtained as a system of simultaneous partial differential equations in terms of three displacement variables (parameters) namely w( x,y,z=0),θ_x (x,y)and θ_y(x,y) where w(x, y, z) is the transverse displacement θ_x and θ_y are rotations of the middle surface. It was shown that when θ_x =-^∂w/_∂x, θ_y=-^∂w/_∂xand k → ∞ where k is the shear correction factor, the Mindlin plate equations reduce to the classical Kirchhoff plate equation which is a biharmonic equation in terms of w(x, y, z = 0).

Keywords: Mindlin plate, Kirchhoff plate, tranverse displacement, rotations, shear correction factor, biharmonic equation.