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Thermal effects in rectangular plate made of rubber, copper and glass materials

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Abstract

The objective of this paper is to present the study of thermal effect in the rectangular plate made of rubber, copper and glass materials using transition theory. The extension and contraction regions presented by the transition points of the differential equation in defining the deformed fields. The analysis also makes the neutral surface separating the two regions. It has been observed that with increased compressibility of materials, the value of neutral axis on the surface of tension must be concentrated on the surface compression. The value of circumferential stress has a maximum at the neutral surface of the rectangular plate made of rubber material in comparison with rectangular plate made of copper and glass materials. With the introduction of thermal effects the value of the circumference as well as radial stresses increases in temperature \(\left( {\Theta_{1} = 0^\circ F,\Theta_{2} = 1000^\circ F} \right)\) and decreases in temperature \(\left( {\Theta_{1} = 700^\circ F,\Theta_{2} = 0^\circ F} \right)\). Rectangular plate made of rubber material is more comfortable than that of copper and glass materials. Numerical results are shown graphically.

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Abbreviations

\(\Theta\) :

Temperature

\(A_{1} ,\,A_{2} ,\,k_{{1}} ,\,k_{{2}}\) :

Constant of integration

E :

Young’s modulus

\(c\) :

Compressibility factor

\(\varepsilon_{rr} ,\,\varepsilon_{zz} ,\,\varepsilon_{\theta \theta }\) :

Strain components

M :

Bending moment

A :

Neutral axis

\(u,\,v,\,w\) :

Displacement components

\(r,\,\theta ,\,z\) :

Radial, circumferential and axial directions

\(\delta_{ij}\) :

Kronecker’s delta

\(\alpha\) :

Coefficient of thermal expansion

v :

Poisson’s ratio

\(\lambda ,\,\mu\) :

Lame’s constants

\(\tau_{ij} ,\varepsilon_{ij}\) :

Stress and strain components

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Funding

This research received no specific Grant from any funding agency in the public, commercial, or not for profit sectors.

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Authors and Affiliations

  1. Department of Mathematics, ICFAI University Himachal Pradesh, Baddi, 174105, India

    Pankaj Thakur

  2. Research Scholar, Department of Mathematics, ICFAI University Himachal Pradesh, Baddi, India

    Monika Sethi & Neeru Gupta

  3. Research Scholar, Department of Physics, ICFAI University Himachal Pradesh, Baddi, India

    Kanav Gupta

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  1. Pankaj Thakur
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  2. Monika Sethi
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  3. Neeru Gupta
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  4. Kanav Gupta
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Correspondence to Pankaj Thakur.

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Thakur, P., Sethi, M., Gupta, N. et al. Thermal effects in rectangular plate made of rubber, copper and glass materials. J Rubber Res 24, 147–155 (2021). https://doi.org/10.1007/s42464-020-00080-6

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