Thermal stress analysis of orthotropic plate containing a rectangular hole using complex variable method

One of the most important issues in the design of engineering structures is the prevention of structural failure due to the stress caused by geometric discontinuities. Hole geometry is one of the effective parameters in the distribution of stress and displacement around it. In this study, using the two-dimensional thermoelastic theory and based on the Likhnitskiiʼ complex variable technique, the stress analysis of orthotropic infinite plate with a circular hole under a uniform heat flux is developed to the plate containing a rectangular hole. To achieve this goal, a conformal mapping function is used to map an infinite plate containing a rectangular hole into the outside of a unit circle. Stress and displacement distributions around the rectangular hole in an orthotropic infinite plate are investigated in thermal steady state condition. The plate is under uniform heat flux at infinity and Neumann boundary conditions and thermal-insulated condition at the edge of the hole are considered. The rotation angle of the hole, fiber angle, the flux angle, bluntness and the aspect ratio of hole size are important parameters investigated in the present study. The obtained results show that these parameters have a significant effect on the stress and displacement distributions around the rectangular hole.