  In this article, we consider the problem of optimal design of a compliant
structure under a volume constraint, within the framework of linear elasticity.
We introduce the pure displacement and the dual mixed formulations of the
linear elasticity problem and we compute the volumetric expressions of the
shape gradient of the compliance by means of the velocity method. A preliminary
qualitative comparison of the two expressions of the shape gradient is
performed through some numerical simulations using the Boundary Variation
Algorithm.
