Thermal Stresses Around a Heated Hole in a Large Glass Plate

The problem of sealing a hole in a cool glass plate under conditions at or above annealing temperatures is examined. By use of the well-known equations for stresses in thin circular disks and the application of proper boundary conditions, the concept of a negative temperature distribution (a method of superposition used in stress analysis) that will represent the cooling leads to the conclusion that, under these conditions, the stress in the glass near the hole is independent of the temperature distribution around the hole and dependent only on the physical constants of the glass and the temperature of the lateral surface of the hole.