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Thermo-Elastic Analysis of Functionally Graded Toroidal Shells

  • Research Article - Mechanical Engineering
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Abstract

Thermo-elastic analysis of a functionally graded toroidal shell under the effect of thermo-mechanical loadings is carried out. Material properties of the toroidal shell are assumed to be isotropic and graded in the radial direction according to a power law function, while the Poisson’s ratio is assumed to be constant. The toroidal shell is considered to be under the effect of general loading conditions including both axisymmetric and asymmetric cases. Semi-analytical solutions of displacement and stress fields are obtained using the Fourier and polynomial differential quadrature methods. Finite element calculations of displacement and stress fields are also carried out and results are compared. Effects of various material grading parameters and the temperature difference across the thickness of the toroidal shell on the distribution of stress and displacement fields are presented. It is found that components of the stress field in a functionally graded toroidal shell are less in magnitude than those corresponding to a homogeneous shell.

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Abbreviations

A (i) :

Weighting coefficients of the ith-order derivative in the radial direction

a :

Inner radius of the shell

B (i) :

Weighting coefficients of the ith-order derivative in the meridional direction

b :

Outer radius of the shell

E :

Young’s modulus

K :

Coefficient of thermal conduction

M, N :

Number of grid points in radial and meridional directions, respectively

p :

Internal pressure

R :

Bend radius of the shell

T(r):

Temperature distribution

u, v :

Displacement components in the radial and meriodinal directions, respectively

α :

Coefficient of thermal expansion

β :

Grading parameter in the radial direction

ε ij :

Components of strain tensor

λ, μ :

The Lamé constants

υ :

Poisson’s ratio

σ ij :

Components of stress tensor

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Authors and Affiliations

  1. Mechanical Engineering Department, Babol University of Technology, P.O.Box 484, Shariati Avenue, Babol, Iran

    R. Akbari Alashti & M. H. Tarahhomi

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  1. R. Akbari Alashti
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  2. M. H. Tarahhomi
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Correspondence to R. Akbari Alashti.

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Akbari Alashti, R., Tarahhomi, M.H. Thermo-Elastic Analysis of Functionally Graded Toroidal Shells. Arab J Sci Eng 39, 2127–2142 (2014). https://doi.org/10.1007/s13369-013-0742-7

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  • DOI: https://doi.org/10.1007/s13369-013-0742-7

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