Thermal Stresses in Elastic Plates With Elliptic Holes

Abstract

The temperature and membrane stress distributions in an elastic square plate with an insulated central elliptic hole are investigated. The temperature varies along coordinates within the plane. The temperature distribution is determined as the solution of the steady state heat conduction equation, then the membrane stresses due to the temperature are analyzed. For both steps, the free edge conditions around the insulated elliptic hole as well as the boundary conditions at the fully restrained outer edges of the plate are satisfied at selected points by the method of least square point matching. The formulation is valid for any arbitrary orientation of the major axis of the elliptic hole. The numerical results for temperature distribution and membrane stresses are presented for two orientations and compared with the corresponding results for a circular hole.