Mathematical solutions for the flexural analysis of Mindlin’s first order shear deformable circular plates
In this work, the problem of first order shear deformable solid circular plate under transverse load was solved mathematically. The problem considered was assumed axisymmetric. The plate and loading were considered axisymmetric. The problem was defined as a boundary value problem of a system of diff...
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doaj-39f4e51026ba43dea2239faba2ca99f02020-11-25T00:09:03ZengJVE InternationalMathematical Models in Engineering2351-52792424-46272018-06-0142507210.21595/mme.2018.1982519825Mathematical solutions for the flexural analysis of Mindlin’s first order shear deformable circular platesCharles Chinwuba Ike0Department of Civil Engineering, Enugu State University of Science and Technology, Enugu State, NigeriaIn this work, the problem of first order shear deformable solid circular plate under transverse load was solved mathematically. The problem considered was assumed axisymmetric. The plate and loading were considered axisymmetric. The problem was defined as a boundary value problem of a system of differential equations of equilibrium in terms of the stress resultants and the stress – resultants – displacement relations. The set of equations were considered simultaneously to express them in variable separable form. The mathematical technique of separation of variables was then used to obtain solutions for the unknown generalised displacements. Specific problems of clamped edge plates and simply supported edge plates under uniformly distributed load and point load at the centre were considered and solved using the same technique of separation of variables. The mathematical expressions obtained showed that in all cases, the deflection was expressible in terms of flexural and shear components. The maximum deflection was found to occur at the plate centre as is expected from the symmetrical nature of the problem. The shear component of the transverse deflection was found to significantly increase with significant increase in the ratio of the plate thickness to the radius (h/r0).https://www.jvejournals.com/article/19825first order shear deformable circular plateshear deformationflexural deformationaxisymmetrical problemdifferential equations of equilibrium |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Charles Chinwuba Ike |
spellingShingle |
Charles Chinwuba Ike Mathematical solutions for the flexural analysis of Mindlin’s first order shear deformable circular plates Mathematical Models in Engineering first order shear deformable circular plate shear deformation flexural deformation axisymmetrical problem differential equations of equilibrium |
author_facet |
Charles Chinwuba Ike |
author_sort |
Charles Chinwuba Ike |
title |
Mathematical solutions for the flexural analysis of Mindlin’s first order shear deformable circular plates |
title_short |
Mathematical solutions for the flexural analysis of Mindlin’s first order shear deformable circular plates |
title_full |
Mathematical solutions for the flexural analysis of Mindlin’s first order shear deformable circular plates |
title_fullStr |
Mathematical solutions for the flexural analysis of Mindlin’s first order shear deformable circular plates |
title_full_unstemmed |
Mathematical solutions for the flexural analysis of Mindlin’s first order shear deformable circular plates |
title_sort |
mathematical solutions for the flexural analysis of mindlin’s first order shear deformable circular plates |
publisher |
JVE International |
series |
Mathematical Models in Engineering |
issn |
2351-5279 2424-4627 |
publishDate |
2018-06-01 |
description |
In this work, the problem of first order shear deformable solid circular plate under transverse load was solved mathematically. The problem considered was assumed axisymmetric. The plate and loading were considered axisymmetric. The problem was defined as a boundary value problem of a system of differential equations of equilibrium in terms of the stress resultants and the stress – resultants – displacement relations. The set of equations were considered simultaneously to express them in variable separable form. The mathematical technique of separation of variables was then used to obtain solutions for the unknown generalised displacements. Specific problems of clamped edge plates and simply supported edge plates under uniformly distributed load and point load at the centre were considered and solved using the same technique of separation of variables. The mathematical expressions obtained showed that in all cases, the deflection was expressible in terms of flexural and shear components. The maximum deflection was found to occur at the plate centre as is expected from the symmetrical nature of the problem. The shear component of the transverse deflection was found to significantly increase with significant increase in the ratio of the plate thickness to the radius (h/r0). |
topic |
first order shear deformable circular plate shear deformation flexural deformation axisymmetrical problem differential equations of equilibrium |
url |
https://www.jvejournals.com/article/19825 |
work_keys_str_mv |
AT charleschinwubaike mathematicalsolutionsfortheflexuralanalysisofmindlinsfirstordersheardeformablecircularplates |
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1725413208492081152 |