EQUILIBRIUM APPROACH IN THEDERIVATION OF DIFFERENTIAL EQUATIONS FOR HOMOGENEOUS ISOTROPIC MINDLIN PLATES
DOI:
https://doi.org/10.4314/njt.362.1280Keywords:
Mindlin plate, Kirchhoff plate, tranverse displacement, rotations, shear correction factor, biharmonic equation.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 where w(x, y, z) is the transverse displacement and are rotations of the middle surface. It was shown that when 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).
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