To cudgel ones brains

from The Collaborative International Dictionary of English v.0.48

Cudgel \Cudg"el\, v. t. [imp. & p. p. {Cudgeled} or {Cudgelled}
   (-?ld); p. pr. & vb. n. {Cudgeling} or {cudgelling}.]
   To beat with a cudgel.
   [1913 Webster]

         An he here, I would cudgel him like a dog. --Shak.
   [1913 Webster]

   {To cudgel one's brains}, to exercise one's wits.
      [1913 Webster]