If I'm given some sort of shape and there is a displacement given but there are no external forces acting on the body, do I still need to write down the traction free boundary conditions or will there only be displacement boundary conditions?
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I suggest that you check this answer first. After that, yes you can have a problem with only displacement boundary conditions. This is not usual, though. – nicoguaro Apr 18 '20 at 02:42
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Ok thanks, I'm gonna make a separate question with a picture included so I can show you what I mean – HokieFan7 Apr 18 '20 at 03:51