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

Okeke Thompson Edozie , Onyeka Festus Chukwudi,Nwa-David Chidobere


In this paper, the bending attributes of a uniformly loaded three-dimensional (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.

Keywords: 3-D plate theory, Exact bending solution, CSFS thick Plate, Trigonometric Displacement Functions

How to cite this article: Okeke Thompson Edozie , Onyeka Festus Chukwudi,Nwa-David Chidobere, Characteristic Trigonometric Function Application to the Direct Variation Method for Clamped, Simply and Freely Supported Plate Under Uniform Load DistributionsJournal of Materials Engineering, Structures and Computation 1(1) 2022 pp. 40-58


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