Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
권호 표지
DOI QR코드

DOI QR Code

STEADY-STATE TEMPERATURE ANALYSIS TO 2D ELASTICITY AND THERMO-ELASTICITY PROBLEMS FOR INHOMOGENEOUS SOLIDS IN HALF-PLANE

  • GHADLE, KIRTIWANT P. (DEPARTMENT OF MATHEMATICS, DR.BABASAHEB AMBEDKAR MARATHWADA UNIVERSITY) ;
  • ADHE, ABHIJEET B. (BASIC SCIENCES AND HUMANITIES DEPARTMENT, MARATHWADA INSTITUTE OF TECHNOLOGY)
  • Received : 2019.11.21
  • Accepted : 2020.03.03
  • Published : 2020.03.25
Download PDF
⟨ Previous Next ⟩

Abstract

The concept of temperature distribution in inhomogeneous semi-infinite solids is examined by making use of direct integration method. The analysis is done on the solution of the in-plane steady state heat conduction problem under certain boundary conditions. The method of direct integration has been employed, which is then reduced to Volterra integral equation of second kind, produces the explicit form analytical solution. Using resolvent- kernel algorithm, the governing equation is solved to get present solution. The temperature distribution obtained and calculated numerically and the relation with distribution of heat flux generated by internal heat source is shown graphically.

Keywords

References

  1. B. Kalynyak, Integration of Equation of One- Dimensional Problems of Elasticity and Thermo-Elasticity for Inhomogeneous Cylindrical Bodies, Journal of Mathematical Sciences, 13 (2000), 1662-1670. https://doi.org/10.1007/BF02674190
  2. V. Makhovikov, Solution of Heat Conduction Problems for a Body of Revolution Mode of Inhomogeneous Materials, Journal of Engineering Physics, 10 (1966), 115-119. https://doi.org/10.1007/BF00833943
  3. J. Nohel, Some Problems in Volterra Integral Equations, Bulletin of the American Mathematical Society, 68 (1962), 323-329. https://doi.org/10.1090/S0002-9904-1962-10790-3
  4. D. Porter, The Solution of Integral Equations with Difference Kernels, Journal of Integral Equations and Applications, 3 (1991), 429-454. https://doi.org/10.1216/jiea/1181075634
  5. A. Rychachivskyy and Y. Tokovyy, Correct Analytical Solutions to the Thermoelasticity problem in a Semi-Plane, Journal of Thermal Stresses, 31 (2008), 1125-1145. https://doi.org/10.1080/01495730802250854
  6. Y. Tokovyy and C. Ma, Steady-State Heat Transfer and Thermo-Elastic Analysis Of Inhomogeneous Semi-Infinite Solids, Heat conduction-Basic Research, (2011), 251-268.
  7. Y. Tokovyy and C. Ma, An Analytical Solution to the Three- Dimensional Problem on Elastic Equilibrium of an Exponentially-Inhomogeneous Layer, Journal of Mechanics, 31 (2015), 545-555. https://doi.org/10.1017/jmech.2015.17
  8. Y. Tokovyy and C. Ma, Three-Dimensional Temperature and Thermal Stress Analysis of an Inhomogeneous Layer, Journal of Thermal Stresses, 36 (2013), 790-808. https://doi.org/10.1080/01495739.2013.787853
  9. V. Vigak and A. Rychachiivskyy, The Method of Direct Integration of the Equations of Three- Dimensional Elastic and Thermoelastic Problems for Space and a Half Space, International Applied Mechanics, 36 (2000), 1468-1475. https://doi.org/10.1023/A:1011356515333
  10. Y. Tokovyy and C. Ma, Thermal Stresses in Anisotropic and Radially Inhomogeneous Annular Domains, Journal of Thermal Stresses, 31 (2008), 892-913. https://doi.org/10.1080/01495730802194433
  11. Y. Tokovyy and C. Ma, Analysis of 2D-Non-axisymmetric Elasticity and Thermoelasticity Problems for Radially Inhomogeneous Hollow Cyllinders, Sringer, New York, 61 (2007), 171-184.
  12. Y. Tokovyy , A. Rychachivskyy, Reduction of Plane Thermoelasticity Problems in Inhomogeneous Strip to Integral Volterra type Equation, Math Modell Anal, 10 (2005), 91-100. https://doi.org/10.3846/13926292.2005.9637274
  13. T. Vasileva, Y. Dudarev, A. Kashin and M. Maksimov, Approximate Methods for Solving Problems of Non Stationary Heat Conduction in Inhomogeneous Media, Journal of Engineering Physics and Thermophysics, 73 (2000), 1317-1322. https://doi.org/10.1023/A:1009463430285
  14. V. Vigak, Correct Solutions of Plane Elastic Problems for a Semi-plane, International Applied Mechanics, 40 (2004), 283-289. https://doi.org/10.1023/B:INAM.0000031910.20827.19
  15. V. Vigak, Method for Direct Integration Of the Equations of an Axisymmetric Problem of Thermo-Elasticity in Stresses for Unbounded regions, International Applied Mechanics, 35 (1999), 262-268. https://doi.org/10.1007/BF02682121
  16. V. Vihak, B. Kalynyak, Reduction of One-Dimensional Elasticity and Thermo-Elasicity Problems in Inhomogeneous and Thermal Sensitive Solids to the Solution of Integral Equation of Volterra Type, Proceeding of the 3rd international Congress on Thermal Stresses, Cracow, Poland, 1999.
  17. V. Vigak and A. Rychachivskyy, Bounded Solutions of Plane Elasticity Problems in Semi-Plane, Journal of Computational And Applied Mechanics, 12 (2001), 263-272.
  18. M. Necati Ozisik, Boundary Value Problems of Heat Conduction, Dover Publications, INC, Mineola, New York, (1968).
  19. I. Sneddon , Fourier Transform, McGraw-Hill Book Company, INC, (1951).