Document Type : Original Research Paper

**Authors**

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

**Abstract**

The fully classical coupled thermoelasticity problem in a thick hollow cylinder is solved using analytical methods. Finite Hankel transform, Laplace transform and a contemporary innovative method are used to solve the problem and presenting closed-form relations for temperature and stress distribution. To solve the energy equation and the structural equation, on the inner and the outer surfaces of the cylinder, time-dependent thermal and mechanical boundary conditions are applied. The Dirichlet boundary condition which represents temperature, is considered to solve the energy equation and the Cauchy boundary condition which represent traction, is considered for the equation of motion. Two cases are studied numerically, pure mechanical load and pure thermal load. In plotting the results for the case of prescribing pure mechanical load in spite of not applying any thermal load induced temperature can be seen in the temperature history figure. Due to solving the elastodynamic problem, the elastic and the thermoelastic stress wave propagation into the medium and the reflection were observed in the plotted results.

**Keywords**

[2] A.R. Shahani, S. Momeni Bashusqeh, Analytical solution of the coupled thermo-elasticity problem in a pressurized sphere, J. Therm. Stresses, 36(12) (2013) 1283-1307.

[3] A.R. Shahani, S.M. Nabavi, Analytical solution of the quasi-static thermoelasticity problem in a pressurized thick-walled cylinder subjected to transient thermal loading, Appl. Math. Model., 31(9) (2007) 1807-1818.

[4] Y. Yun, I.Y. Jang, L. Tang, Thermal stress distribution in thick wall cylinder under thermal shock, J. Press. Vessel Technol., 131(2) (2009) 021212.

[5] M. Raoofian Naeeni, M. Eskandari-Ghadi, A.R. Ardalan, M. Rahimian, Y. Hayati, Analytical Solution of Coupled Thermoelastic Axisymmetric Transient Waves in a Transversely Isotropic Half-Space, J. Appl. Mech., 80(2) (2013) 024502.

[6] W. Liang, S. Huang, W.S. Tan, Y.Z. Wang, Asymptotic approach to transient thermal shock problem with variable material properties, Mech. Adv. Mater. Struct., 26(4) (2019) 350-358.

[7] X. Wang, Thermal shock in a hollow cylinder caused by rapid arbitrary heating, J. Sound Vib., 183(5) (1995) 899-906.

[8] H. Cho, G.A. Kardomateas, C.S. Valle, Elastodynamic solution for the thermal shock stresses in an orthotropic thick cylindrical shell, J. Appl. Mech., 65(1) (1998) 184-193.

[9] H.J. Ding, H.M. Wang, W.Q. Chen, A solution of a non-homogeneous orthotropic cylindrical shell for axisymmetric plane strain dynamic thermoelastic problems, J. Sound Vib., 263(4) (2003) 815-829.

[10] J. Zhou, Z. Deng, X. Hou, Transient thermal response in thick orthotropic hollow cylinders with finite length: high order shell theory, Acta Mech. Solida Sin., 23(2) (2010) 156-166.

[11] S.S. Vel, Exact thermoelastic analysis of functionally graded anisotropic hollow cylinders with arbitrary material gradation. Mech. Adv. Mater. Struct., 18(1) (2011) 14-31.

[12] M. Marin, On the domain of influence in thermoelasticity of bodies with voids, Arch. Math., 33(4) (1997) 301-308.

[13] A.V. Rychahivskyy, Y.V. Tokovyy, Correct analytical solutions to the thermoelasticity problems in a semi-plane, J. Therm. Stresses, 31(11) (2008) 1125-1145.

[14] A.R. Shahani, H. Sharifi Torki, Analytical solution of the thermoelasticity problem in thick-walled cylinder subjected to transient thermal loading, Modares Mechanical Engineering, 16(10) (2016) 147-154.

[15] A.R. Shahani, H. Sharifi Torki, Determination of the thermal stress wave propagation in orthotropic hollow cylinder based on classical theory of thermoelasticity, Contin. Mech. Thermodyn., 30(3) (2018) 509-527.

[16] J.Q. Tarn, Exact solutions for functionally graded anisotropic cylinders subjected to thermal and mechanical loads, Int. J. Solids Struct., 38(46) (2001) 8189-8206.

[17] C. Itu, C. Itu, A. Ochsner, S. Vlase, M. Marin, Improved rigidity of composite circular plates through radial ribs, Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications. 233(8) (2018) 1585-1593.

[18] P. Lata, I. Kaur, Thermomechanical interactions in transversely isotropic thick circular plate with axisymmetric heat supply, Struct. Eng. Mech., 69(6) (2019) 607-614.

[19] S. Vlase, M. Marin, AOchner, M.L. Scutaru, Motion equation for a flexible one-dimensional element used in the dynamical analysis of a multibody system, Continuum Mech. Thermodyn., 31(1) (2018) 715-724.

[20] K.C. Mishra, J.N. Sharma, P.K. Sharma, Analysis of vibrations in a non-homogeneous thermoelastic thin annular disk under dynamic pressure, Mech. Based Des. Struct. Mach., 45(2) (2017) 207-218.

[21] D.K. Sharma, D. Thakur, V. Walia, N. Sarkar, Free vibration analysis of a nonlocal thermoelastic hollow cylinder with diffusion, J. Therm. Stresses, 43(8) (2020) 981-997.

[22] I.A. Abbas, Analytical solution for a free vibration of a thermoelastic hollow sphere, Mech. Based Des. Struct. Mach., 43(3) (2015) 265-276.

[23] N. Noda, R.B. Hetnarski, Y. Tanigawa, Thermal Stresses, New York: Taylor & Francis, (2003).

[24] I.N. Sneddon, The Use of Integral Transform, New York: Mc-Graw-Hill Book Company, (1972).

[25] G. Cinelli, An extension of the finite hankel transform and applications, Int. J. Eng. Sci., 3(5) (1965) 539-559.

[26] M. Jabbari, H. Dehbani, M.R. Eslami, An exact solution for classic coupled thermoelasticity in cylindrical coordinates, J. Press. Vessel Technol., 133(1) (2011) 051204.

September 2020

Pages 121-134