Thermal deflection and thermal stresses in a thin circular plate under an axisymmetric heat source

Motivated by the need to investigate thermal effects on the deflection and stresses in a thin-wall workpiece during machining, the thermal problem is modeled with an axisymmetric input to emulate the heat generated at the tool-workpiece interface in a turning process. Using a compressor disk as an illustrative example, the boundary value problem is formulated with a plate model where the perimetric edge is clamped and insulated, and the upper and lower surfaces are subjected to heat convection. The closed form solution of temperature distribution is obtained via Green's function method, based on which the thermal deflection/stresses are obtained in serial forms from the plate constitutive relations. The obtained solutions have been numerically verified with finite-element analysis (FEA), where simulations have been performed for three different materials with discrepant thermomechanical properties to study the thermal effects on the induced deflection and stresses. The analytical result is justified by its good agreement with FEA and its time efficiency in computation offers advantages in potential real-time application to manufacturing process monitoring.