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Elastic–plastic stresses in a rotating disc of transversely isotropic material fitted with a shaft and subjected to thermal gradient

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Abstract

The elastic–plastic stresses in a rotating disc of transversely isotropic material fitted with a shaft and subjected to thermal gradient has been analyzed by using Seth’s transition theory and generalized strain measure. It has been observed that disc made of beryl and magnesium materials requires higher angular speed to yield at the inner surface in comparison to the disc made of brass material. The radial stress has a maximum at the internal surface of the disc made of beryl, magnesium and brass materials, but circumferential stress neither maximum nor minimum at this surface. With the introduction of thermal effect, the value of circumferential stress has a maximum at the external surface of the disc made of the beryl and magnesium, but the reverse results are obtained for the disc made of brass material. The combined impacts of temperature and angular speed have been displayed numerically and depicted graphically.

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Abbreviations

\(r_{i}\) :

Inner radius (m)

\(r_{o}\) :

Outer radius (m)

\(A,B,k_{1} ,k_{2} ,d\) :

Constants (dimensionless)

\(c_{ij}\) :

Material constants (N/m2)

\(e_{ij}\) :

Strain tensor (dimensionless)

\(n\) :

Strain measure coefficients (dimensionless)

\(u,v,w\) :

Displacement components (m

\(\alpha_{ij}\) :

Thermal expansion coefficient (1/°F)

\(\eta\) :

Function of r only

\(\rho\) :

Density (Kg/m3)

\(\tau_{ij}\) :

Stress tensor (N/m2)

\(\beta_{i}\) :

Thermal moduli (N/m2 °F)

\(\Theta\) :

Temperature (°F)

\(\zeta\) :

Transition function

\(\omega\) :

Angular velocity (1/s)

\(\Omega^{2}\) :

Speed factor (dimensionless)

Y, Y * :

Yieldings stresses

E :

Young’s modulus (Nm−2)

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Authors and Affiliations

  1. Department of Mathematics, ICFAI University, Baddi, Himachal Pradesh, India

    Pankaj Thakur, Naresh Kumar & Monika Sethi

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  1. Pankaj Thakur
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  2. Naresh Kumar
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  3. Monika Sethi
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Correspondence to Pankaj Thakur.

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Thakur, P., Kumar, N. & Sethi, M. Elastic–plastic stresses in a rotating disc of transversely isotropic material fitted with a shaft and subjected to thermal gradient. Meccanica 56, 1165–1175 (2021). https://doi.org/10.1007/s11012-021-01318-2

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  • DOI: https://doi.org/10.1007/s11012-021-01318-2

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