My paper “Tulczyjew triples and higher Poisson/Schouten structures on Lie algebroids” arXiv:0910.1243v4 [math-ph] is going to appear in Reports on Mathematical Physics, Vol. 66, No 2, (2010).

Abstract
We show how to extend the construction of Tulczyjew triples to Lie algebroids via graded manifolds. We also provide a generalisation of triangular Lie bialgebroids as higher Poisson and Schouten structures on Lie algebroids.