The real model has welds probably so has a taper at that corner. You can make small solid bodies with swept triangle shape to represent the welds, and use contact to connect to the solid.Or maybe an MPC bonded contact from edge-to-face can resolve the stress singularity, even without solid bodies to represent the welds, since the constraints will connect outward an additional layer of nodes.
If you want to specify a greater thickness to the shell just near the bond point, there are many ways to split the shell body or face. What CAD system does the geometry originate? You can draw a sketch line on the surface and split by that or split by a plane, or by two point selection on the boundary edges. Or you can split entirely in Mechanical using Virtual Topology. Right click on Model in the Outline to insert a Virtual Topology. This allows splitting and merging of faces and edges. If you split in the CAD Modeler you can split just the face so it is multiple faces in the same body, or you can split the body entirely, in which case, you can connect with shared topology if you use SpaceClaim or DesignModeler. In Mechanical you can, of course, set a different thickness on different bodies if you split the body entirely. If you split only the face, so as to have multiple faces in the same body, then you can right click in Mechanical on "Geometry > Insert > Thickness." This allows you to select faces and set different thicknesses for faces in the same body.