Thermal Stress Concentration Problem in the Plate with a Slit

Abstract

Thermal stress concentration at the slit or the crack in a finite region occurs in many engineering problems. For such problems, the use of the finite difference or finite element technique brings in a large number of linear simultaneous equations, and so solving these equations is very time-consuming. Especially, the case of approximate crack-formed slit is more difficult due to divergency of the solution and it is almost impossible to obtain the correct solution for that case. In this paper, therefore, the analysis is developed by means of the point-matching technique in the elliptic coordinate, and the solutions are obtained on the rate of stress concentration for slits having the ratio of the major axis to the minor axis of ellipse up to 35. Numerical examples are shown for the problems in a square plate with many different shaped types of slit formed by an elliptical hole under heat generation.