Starting from version 2.0, UML introduced hierarchical composite structures, which are an expressive way of defining complex software architectures, but which have a very loosely defined semantics in the standard. In this paper we propose a set of consistency rules that disambiguate the meaning of UML composite structures. Our primary goal was to have an operational model of composite structures for the OMEGA UML profile, an executable profile dedicated to the formal specification and validation of real-time systems, developed in a past project to which we contributed. However, the rules and principles stated here are applicable to other hierarchical component models based on the same concepts, such as SysML. The presented ruleset is supported by an OCL formalization which is described in this report. This formalization was applied on different complex models for the evaluation and validation of the proposed principles.