Did you try to assign the Lumped RLC boundary to non-rectangular sheets in the eigenmode simulations?
HFSS Help document says "HFSS assumes the lumped RLC is assigned to a rectangular face. If you assign a non-rectangular face, HFSS issues a warning, but proceed with the solution. Using a non-rectangular face can result in less accurate representation of the lumped RLC".
It implies that you can assign the Lumped RLC boundary to non-rectangular sheets also but accuracy will be compromised to some extent.
Hope this will help.
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