This paper deals with the shape design sensitivity analysis of domain-dependent functionals that arise in optimal compliance design for simultaneous optimization of material and structure. Recent work has shown that, for a representation of material properties in the most general form possible, analytical forms of the optimized compliance functionals can be derived. It is these functionals that are considered. The reduced structural optimization problem is considered in a displacements-only formulation and in a stress-based sizing design formulation, covering the possibility of mechanical contact in both cases. The analysis provides the necessary information for considering a combination of classical shape design and the possibility of topology design using extremal materials, offering among others the possibility to consider pressure loads in topology design.
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