Exact Solution to Elastic Behavior of Periodic Heat Generating Solid Cylinder

Abstract

The objective of this study is to develop analytical solution of thermally induced stress and deformation in a periodic heat generating solid cylinder. The cylinder is initially at zero temperature, but for times greater than zero, heat is generated and consumed internally at a time dependent rate. The solution of this complicated problem consists of two parts. In the first part, transient heat conduction equation is formulated and solved by the use of Duhamel's theorem. The second part on the other hand consisted of the formulation of governing elastic equation coupled with the temperature gradient. This equation is nothing but the thermoelastic equation of the cylinder. Analytical solution of the thermoelastic equation reveals the distributions of stress, strain and displacement within the cylinder at a given time instant. Two different periodic functions are handled to describe periodic heat generation in the cylinder. Although periodic, the second function eventually decays to zero

Keywords

• Transient heat generation, periodic heating, Duhamel’s theorem, thermoelasticity, generalized plane strain