A theoretical framework is developped leading to a sound derivation of
Periodic Boundary Conditions (PBCs) for the analysis of domains smaller then
the Unit Cells (UCs), named reduced Unit Cells (rUCs), by exploiting
non-orthogonal translations and symmetries. A particular type of UCs,
Offset-reduced Unit Cells (OrUCs) are highlighted. These enable the reduction
of the analysis domain of the traditionally defined UCs without any loading
restriction. The relevance of the framework and its application to any periodic
structure is illustrated through two practical examples: 3D woven and
honeycomb.