Exact solutions for variable-thickness inhomogeneous elastic plates under various boundary conditions |
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Authors: | A M Zenkour D S Mashat |
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Institution: | (1) Department of Mathematics, Faculty of Science, King AbdulAziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia;(2) Department of Mathematics, Faculty of Education, Kafr El-Sheikh University, Kafr El-Sheikh, 33516, Egypt |
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Abstract: | In this paper, an exact solution to the governing equations of the bending of a variable-thickness inhomogeneous rectangular
plate is presented. The procedure is applicable to variable-thickness inhomogeneous rectangular plates with two opposite edges
simply supported. The remaining ones subjected to a combination of clamped, simply supported, and free boundary conditions
and between these two edges the plate may have varying thickness. The procedure is valuable in view of the fact that tables
of deflections and stresses cannot be presented for variable-thickness inhomogeneous orthotropic plates as for uniform-thickness
homogeneous isotropic plates even for commonly encountered loads because the results depend on the inhomogeneity coefficient
and the orthotropic material properties instead of a single flexural rigidity. Numerical results, useful for the validation
or otherwise of approximate solutions, are tabulated. The influences of the degree of the inhomogeneity, aspect ratio, thickness
parameter and degree of non-uniformity on the deflections and stresses are investigated.
This paper is partially supported by the Deanship of Scientific Research at King AbdulAziz University (Grant no. 172/427). |
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Keywords: | Variable-thickness Inhomogeneous Orthotropic Boundary conditions |
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