Numerical simulations of temperature distribution and strain in a cylinder subjected alternately to heating and cooling

摘要

Sagar and Payne [1] in 1974 presented solutions for the transient temperature distribution and for stresses and strains under the combined mechanical and thermal loading. They analyzed the accumulation of plastic strain over cycles of heating and cooling of the outer surface of a loaded thick-walled circular cylinder under pure axial torsion and a combination of torsion and tension. They employed numerical integration to calculate plastic strains by using the trapezoidal rule. They sought the solution of the transient temperature distribution in closed form by using the Green's function. This paper presents the techniques of using MATLAB PDE solver to solve the transient temperature distribution that is in turn used to perform the numerical integration to calculate the total strain by the trapezoidal rule in an easier and more efficient numerical method of solution in contrast with the theoretical and mathematical analysis by Sagar and Payne. It illustrates the straightforward formulation, solution, and plotting of the solution of an initial-boundary value for a partial differential equation in one spatial variable r and the time t. The numerical results are confirmed with those in Reference [2].