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Dynamic analysis of thick short length FGM cylinders

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Abstract

In this paper a thick short length hollow cylinder made of functionally graded materials (FGMs) under internal impact loading is considered. The inner surface of the cylinder is pure ceramic, the outer surface is pure metal, and the material composition varies continuously along its thickness. Finite Element Method based on Rayleigh-Ritz energy formulation has been applied to study the propagation of elastic waves in FG thick hollow cylinders. The Newmark direct integration method is applied to solve the time dependent equations. The time histories of displacements, stresses, wave propagation in two directions and velocities of radial stress wave propagation for various values of volume fraction exponent have been investigated. Also by using fast Fourier transform, the first natural frequencies for FG cylinders with simply-simply and clamped-clamped ends conditions are illustrated. The model has been compared with result of a plane strain FG thick hollow cylinder which is subjected to an internal impact loading, and it shows very good agreement.

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Author information

Authors and Affiliations

  1. Mechanical Engineering Department, Amirkabir University of Technology, Tehran, 1591634311, Iran

    Kamran Asemi & Mehdi Akhlaghi

  2. Mechanical Engineering Department and Concrete Technology and Durability Research Centre, Amirkabir University of Technology, Tehran, 1591634311, Iran

    Manouchehr Salehi

Authors
  1. Kamran Asemi
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  2. Mehdi Akhlaghi
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  3. Manouchehr Salehi
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Corresponding author

Correspondence to Mehdi Akhlaghi.

Appendix

Appendix

For the simplex linear triangular element the following formulation is used.

(A.1)
(A.2)
(A.3)

The constants a, b and c are defined in terms of the nodal coordinates and A is the area of the element.

(A.4)
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(A.6)
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(A.8)
(A.9)
(A.10)
(A.11)
(A.12)
(A.13)
(A.14)

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Asemi, K., Akhlaghi, M. & Salehi, M. Dynamic analysis of thick short length FGM cylinders. Meccanica 47, 1441–1453 (2012). https://doi.org/10.1007/s11012-011-9527-9

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  • DOI: https://doi.org/10.1007/s11012-011-9527-9

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