Characteristic Trigonometric Function Application to the Direct Variation Method for Clamped, Simply and Freely Supported Plate Under Uniform Load Distributions

Abstract

In this paper, the bending attributes of a uniformly loaded threedimensional (3-D) plate are modelled using exact trigonometric shape
functions; the effects of shear correction factors associated with refined
plate theory (RPT) are obviated. As an advancement of the RPT theory,
the equations of equilibrium of the current model were obtained from
fundamental principles of elasticity by applying the three-dimensional
(3-D) kinematic deformation and constitutive relations which results of
the six stress components. The formulated 3-D kinematics and
constitutive relations was used to obtain the energy equation which was
later transformed into compatibility equation to determine the function
of deflection and rotation The governing equations were obtained and
solved in terms of trigonometry to get the exact deflection function of the
plate. The rotation and deflection function were substituted into the
energy equation to get the coefficients of deflection and rotation.
Thereafter, these coefficients were substituted into the obtained
displacement and stress equations to get the model for evaluating the
bending of thick plates that was clamped on the first edge, free at the
third edge, with the second and fourth edges simply supported
respectively (CSFS). The recorded outcome confirms that the values for
stresses and displacement obtained from this 3-D theory is more
accurate and reliable compared to refined plate theories applied in
previous studies. The overall average percentage differences between
the present study and the studies by Onyeka (2021) and Gwarah (2019)
for center deflection of a square plate was 4.8%. This showed about 95%
confidence level for adoption of 3-D plate analogy which is required as
the only reliable modeling theory for an exact bending solution of thick
plates as unrealistic solutions are obtained from 2D shear deformation
theories.