Courant algebroid without constraints on fluxes on its Dirac structures

We consider the standard Courant algebroid and show how the $O(D,D)$ group elements give rise to the family of Courant algebroids, defined with different twisted Courant brackets. With the appropriate transformation of the anchor, we show that all Courant algebroid relations are a priori satisfied. We analyze a couple of Courant algebroids relevant for string theory and their respective Dirac structures, obtaining constraints they impose on fluxes. In the end, we show that the Courant algebroid that is simultaneously twisted by both B and θ is characterized by Dirac structures with no restrictions imposed on fluxes.