# Thermoelastic Stress Analysis Perfectly Clamped Metallic Rod Using Integral Transform Technique

• G. R. Gandhe
• V. S. Kulkarni
• Y. M. Ghugal
Conference paper

## Abstract

This manuscript deals with thermoelastic stress analysis of perfectly clamped metallic rod of length, l. The metallic rod is subjected to arbitrary temperature, $$T_{1 }$$ at the terminal end of rod, $$x = l$$. The initial end of rod, x = 0 is thermally insulated. Initially, the metallic rod is at non-zero constant temperature, $$T_{0 }$$. Under these conditions, the temperature distribution and the thermal stress developed within the metallic rod are required to be determined. The mathematical solution of heat conduction equation is obtained by integral transform technique which gives analytical solution for temperature distribution in series form. The convergence analysis of series solution is done. The result obtained for temperature distribution and thermal stresses are expressed in the form of analytical solution and corresponding numerical results for steel rod are shown graphically and illustrate technically.

## Keywords

Temperature change Thermal stresses Integral transform technique

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## Authors and Affiliations

• G. R. Gandhe
• 1
• V. S. Kulkarni
• 2
• Y. M. Ghugal
• 3
1. 1.Deogiri Institute of Engineering and Management StudiesAurangabadIndia
2. 2.Mumbai UniversityMumbaiIndia