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Ibearugbulem, O. M.
Department of Civil Engineering, Federal University of Technology, Owerri, Nigeria
Ettu, L. O.
Department of Civil Engineering, Federal University of Technology, Owerri, Nigeria
Anya, C. U.
Department of Civil Engineering, Federal University of Technology, Owerri, Nigeria
Chukwudi, P. E.
Department of Civil Engineering, Federal Polytechnic Nekede, Owerri, Nigeria
ABSTRACT
This work conducted a bending analysis of a thin
simply supported rectangular plate subjected to varying loads using energy
approach. The varying load considered is a triangular transverse load
(hydrostatic). It was achieved by the application of the displacement field,
kinematic and constitutive relations. The constitutive relations were
substituted in the strain energy equation and then the total potential energy
function was obtained as the difference between the strain energy of the plate
and the external work done by the varying load. The potential energy function
was minimized with respect to the deflection function and this gave the
deflection equation in a polynomial form. This deflection is a function of two
orthogonal deflection functions in the directions of x and y. It was later
simplified as a product of the amplitude of deflection, A, and shape function,
h. The formula for the amplitude of deflection was obtained by minimizing the
total potential energy function with respect to the amplitude. The deflection
shape function equation for the plate was derived. Based on the deflection
equation obtained, the formulas for the in-plane stresses, moments and shear
forces were derived. Numerical applications were performed using aspect ratio,
β (that is b/a) ranging from 1.0 to 2.0. The Poisson’s ratio used is 0.3.
Results obtained in this present work were compared with those of a previous
work done by Timoshenko and Woinowsky-Krieger, the percentage difference of the
central deflection coefficients ranges from 2.82 to 4.89 as the aspect ratio
increases from 1.0 to 2.0. It was observed that the percentage differences are
within acceptable ranges. Hence, Energy approach with orthogonal polynomial
deflection function can be used to carry out bending analysis on thin plate
subjected to varying loads.
Keywords: Thin Plates, Varying Loads, Energy Approach, Bending Analysis
https://doi.org/10.33922/j.ujet_v9i2_4
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Published
Monday, November 06, 2023
Issue
Vol.9 No.2, December 2023
Article Section
GENERAL
The contents of the articles are the sole opinion of the author(s) and not of UJET.
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