Thermal stress analysis in metallic plates with a non-circular hole subjected to uniform heat flux

• An analytical solution provided numerical results to obtain the normalized stress of perforated isotropic plates.
• The normalized stresses can be significantly varied by changing the hole shape, bluntness and hole orientation.
• For a specific bluntness, the desirable stresses are less than the desirable stress of similar plates with a circular hole.
• In addition to the bluntness, the rotation angle of hole also has a significant impact in reducing the normalized stress.
• In a wide range of rotation angle, the desirable stress of the non-circular holes is less than those of a circular hole (w = 0).

The purpose of this study is to evaluate stress distribution around a non-circular hole in an infinite metallic plate subjected to a uniform heat flux. The development of the Goodier and Florence’s method is used for the stress analysis of perforated plates subjected to a uniform heat flux. Goodier and Florence used their solution for the stress analysis of infinite isotropic plates with circular and elliptical holes. In order to expand their method to study non-circular holes, by means of conformal mapping, the infinite area external to the hole can be presented by the area outside the unit circle. In this study, thermal-insulated condition along the hole boundary is assumed. The rotation angle of hole, bluntness and the angle of heat flux as important parameters are considered in this study. Results showed that the effects of these parameters on stress distribution around various shaped holes are very significant and by the correct selection of these parameters, a lower amount of thermal stress compare to that of a circular hole can be achieved.