Vibration and Stability Analysis of Functionally Graded Skew Plate Using Higher Order Shear Deformation Theory

Vibration and Stability Analysis of Functionally Graded Skew Plate Using Higher Order Shear... This paper deals with the vibration and buckling analysis of skew functionally graded material (FGM) plates. A finite element mathematical model is developed based on higher order shear deformation theory. The model is based on an eight noded isoparametric element with seven degrees of freedom per node. The material properties are graded along thickness direction obeying simple power-law distribution. The general displacement equation provides $$\hbox {C}^{0}$$ C 0 continuity. The transverse shear strain undergoes parabolic variation through the thickness of the plate. Hence, there is no requirement of a shear correction factor in this theory. The governing equation for the skew FGM plate is obtained using Hamilton’s principle. The obtained results are compared with the published results to determine the accuracy of the method. The effect of various parameters like aspect ratio, side-thickness ratio, volume fraction index, boundary conditions and skew angle on the natural frequencies and buckling loads has been investigated. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Applied and Computational Mathematics Springer Journals

Vibration and Stability Analysis of Functionally Graded Skew Plate Using Higher Order Shear Deformation Theory

, Volume 4 (1) – Dec 2, 2017
22 pages

Publisher
Springer Journals
Copyright © 2017 by Springer (India) Private Ltd., part of Springer Nature
Subject
Mathematics; Applications of Mathematics; Mathematical Modeling and Industrial Mathematics; Operations Research/Decision Theory; Theoretical, Mathematical and Computational Physics; Computational Science and Engineering; Nuclear Energy
ISSN
2349-5103
eISSN
2199-5796
D.O.I.
10.1007/s40819-017-0440-3
Publisher site
See Article on Publisher Site

Abstract

This paper deals with the vibration and buckling analysis of skew functionally graded material (FGM) plates. A finite element mathematical model is developed based on higher order shear deformation theory. The model is based on an eight noded isoparametric element with seven degrees of freedom per node. The material properties are graded along thickness direction obeying simple power-law distribution. The general displacement equation provides $$\hbox {C}^{0}$$ C 0 continuity. The transverse shear strain undergoes parabolic variation through the thickness of the plate. Hence, there is no requirement of a shear correction factor in this theory. The governing equation for the skew FGM plate is obtained using Hamilton’s principle. The obtained results are compared with the published results to determine the accuracy of the method. The effect of various parameters like aspect ratio, side-thickness ratio, volume fraction index, boundary conditions and skew angle on the natural frequencies and buckling loads has been investigated.

Journal

International Journal of Applied and Computational MathematicsSpringer Journals

Published: Dec 2, 2017

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