Elastodynamic Solution for Plane-Strain Response of Functionally Graded Thick Hollow Cylinders by Analytical Method

Mehdi Nikkhah; Farhang Honarvar; Ehsan Dehghan

doi:10.3879/j.issn.1000-0887.2011.02.006

Volume 32 Issue 2

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Mehdi Nikkhah, Farhang Honarvar, Ehsan Dehghan. Elastodynamic Solution for Plane-Strain Response of Functionally Graded Thick Hollow Cylinders by Analytical Method[J]. Applied Mathematics and Mechanics, 2011, 32(2): 180-193. doi: 10.3879/j.issn.1000-0887.2011.02.006

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Elastodynamic Solution for Plane-Strain Response of Functionally Graded Thick Hollow Cylinders by Analytical Method

doi: 10.3879/j.issn.1000-0887.2011.02.006

Faculty of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran

Received Date: 2010-10-24
Rev Recd Date: 2010-11-22
Publish Date: 2011-02-15

Abstract

Abstract

An elastodynamic solution for the plane-strain response of functionally graded thick hollow cylinders subjected to uniformly-distributed dynamic pressures at the boundary surfaces,was presented. The material properties,except Poisson's ratio,were assumed to vary through the thickness following a power law function. To achieve an exact solution,the dynamic radial displacement was divided into two quasistatic and dynamic parts. For each part,an analytical solution was derived. Firstly,the quasi-static solution was obtained by means of Euler's equation,and then the dynamic solution was derived by utilizing the separation of variables method and the orthogonal expansion technique. Radial displacement and stress distributions were plotted for various FGM hollow cylinders under different dynamic loads and the advantages of the presented method were discussed. The presented analytical solution was suitable for analyzing various arrangements of FGM hollow cylinders with arbitrary thickness and arbitrary initial conditions, subjected to arbitrary form of dynamic pressures distributed uniformly at the boundary surfaces. Finally, radial displacement and stress distributions were plotted for various FGM hollow cylinders under different dynamic loads and the advantages of the presented method were considered.
- functionally graded materials,
- elastodynamic solution,
- hollow cylinders,
- power law function

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References(34)

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