Article Sidebar

Submitted
August 3, 2021
Accepted
February 1, 2022
Published
March 13, 2022
Download
pdf
Statistic
Read Counter : 581 Download : 632

Downloads

Download data is not yet available.

Main Article Content

Abstract

The term thermal stresses are related to mechanics of materials. The thermal stress is formed due to any changes in temperature of a material. The large change in temperature concludes to higher the thermal stresses. Also, there is an effect of thermal expansion coefficient on thermal stresses. The thermal expansion coefficient is different for different materials. In the present paper, the design of a mathematical model concerning the thermal stresses in hollow cylinder subject to the heat conduction with initial and boundary conditions have developed. The basic aim of this work is related to calculations of thermal stresses and thermoelastic displacement in the hollow cylinder by using the reduced differential transform method. The analytical solution is satisfied with the aim of special cases for the copper material properties. The numerical results are illustrated graphically by using mathematical software SCILAB.

Keywords

Thermal stresses Radial displacement Heat conduction Reduced differential transform SCILAB

Article Details

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

How to Cite
Pimpare, S. B., & Sutar, C. S. (2022). Hollow Cylinder with Thermoelastic Modelling by Reduced Differential Transform. Journal of the Indonesian Mathematical Society, 28(1), 8–18. https://doi.org/10.22342/jims.28.1.1036.8-18
Download Citation
Endnote/Zotero/Mendeley (RIS)
BibTeX
Crossref
Scopus
Google Scholar
Europe PMC

References

  1. Abd-Alla, A. M., Yahya, G. A. and Farhan, A. M., Thermal stresses in an infinite circular cylinder, Journal of Mechanical Science and Technology, 26(6) (2012), 1829-1839.
  2. Al-Amr, M.O., New applications of reduced differential transform method, Alexandria Engineering Journal, 53 (2014), 243-247.
  3. Bildik, N. and Konuralp, A., The use of variational iteration method, differential transform method and Adomian decomposition method for solving different types of nonlinear partial differential equations, International Journal of Nonlinear Sciences and Numerical Simulation 7(1) (2006), 65-70.
  4. Boley, B. A. and Weiner, J. H., Theory of Thermal Stresses, New York, 1960.
  5. Elsheikha, A. H., Guo, J. and Lee, K. M., Thermal deflection and thermal stresses in a thin circular plate under an axisymmetric heat source, Journal of Thermal Stresses, 42(3) (2019), 1-13. https://doi.org/10.1080/01495739.2018.1482807
  6. Keskin, Y. and Oturanc, G., Reduced differential transform method for partial differential equation, International Journal of Nonlinear Sciences and Numerical Simulation, 10(6) (2009), 741-749.
  7. Keskin, Y. and Oturanc, G., Application of reduced differntial transformation method for solving gas dynamic equation, Int. J. Contemp. Math. Sciences, 5(22) (2010), 1091-1096.
  8. Mallick, A., Ranjan R. and Sarkar, P. K., Effect of heat transfer on thermal stresses in an annular hyperbolic fin: an approximate analytic solution, Journal of Theoretical and Applied Mechanics, 54(2) (2016), 437-448.
  9. Noda, N. Hetnarski, R.B. , Tanigawa. Y. Thermal Stresses, Taylor and Francis, 2003.
  10. Nowacki, W.,The state of stresses in a thick circular plate due to temperature field, Bulletin of Polish Academy of Sciences Series Technical Sciences, 5 (1957), Article 227.
  11. Ozisik, M., Heat Conduction (Second Edition), John Wiley and Sons, Inc. 1993.
  12. Roychoudhary S. K., A note of quasi static stress in a thin circular plate due to transient temperature applied along the circumference of a circle over the upper face, Bulletin del’Academie Polanaise des Sciences Serie des Sciences Tech. (1972), 20-21.
  13. Sherief, H. H. and Anwar, M. N., Two dimensional generalized thermoelasticity problem for an infinitely long cylinder, Journal of Thermal Stresses, 17(2) (1994), 213-227.
  14. Srivastava, V. K., Mukesh, Awasthi, K., Chaurasia, R. K., Reduced differential transform method to solve two and three dimensional second order hyperbolic telegraph equations, Journal of King Saud University-Engineering Sciences, 29 (2017), 166-171.
  15. Sutar, C. S. and Patil, S. N., Effect of thermal stresses and reduced differential transform on bending of the rectangular plate, J. Indones. Math. Soc., 27(02) (2021), 199-211.
  16. Taghavi, A., Babaei, A. and Mohammadpour, A., Application of reduced differential transform method for solving nonlinear reaction-diffusion-convection problems, An International Journal Applications and Applied Mathematics, 10(1) (2015), 162-170.
  17. Taha, B.A., The use of reduced differential transform method for solving partial differential equations with variable coefficients, Journal of Basrah Researches (Sciences), 37(4) (2011), 226-233.
  18. Takeuti, Y.,Thermal stresses in circular disc due to instantaneous line heat source, ZAMM, 45(4) (1965), 177-184.
  19. Tasi, Y. M.,Thermal stresses in transversely isotropic medium containing a penny-shaped crack, ASME J. Appl. Mech., 50 (1993), 24-28.
  20. Tikhe, A. K. and Deshmukh, K. C., Inverse heat conduction problem in a thin circular plate and its thermal deflection. Appl. Mathemat. Model., 30(6) (2006), 554-560