Distortion generated by a moving weld pool of elliptical cross section in the welding of thin metal sheets

Much analytical work exists dealing with distortion in thin metallic sheets produced by moving heat sources. We consider here the case of the distortion generated in a weld pool whose cross section is in the form of an ellipse in a thin sheet of metal, but with some allowance for variations through the thickness of the material. An essential feature is the presence of this molten pool. The presence of the molten region ensures that stresses arising from viscous flow and pressure are many orders of magnitude smaller then those present in the solid region and can therefore be neglected. In the present analysis all deformations that arise are associated with the equations of linear thermoelastic theory. The problem is tackled analytically and expressions obtained for the stresses in the work piece.