Best Adhesive to Anchor Lenovo U160 Hinge

My daughter has a Lenovo IdeaPad U160, which is basically a fairly powerful subnotebook (circa 2010) in a netbook case. Its lid broke loose from the right hinge, and as difficult as this may be to believe, when I took it apart, I discovered that the hinges are secured to the inside of the screen with adhesive, not screws! It looks like the adhesive was applied to the metal hinges, which were then pressed onto a thin plate made of aluminum plies - or maybe just the ply right behind the screen is aluminum and there are some other materials sandwiched in to give some rigidity to the back of the lid. On the right side, the ply to which the hinge was originally glued had literally torn off - the ply material was still stuck to the hinge.

I first tried to glue it back using Super Glue (cyanoacrilate), and that held for a couple of months, but the twisting force of opening and closing the lid eventually broke it loose again. (Cynanoacrilate holds very well against attempts to pull the bond apart, but not so well against twisting force.) Can anyone suggest an adhesive that's at least as strong as what Lenovo originally used?

Mark Lebowitz
Chicago, IL