A mathematical framework for reducing the domain in the mechanical analysis of periodic structures

Details A mathematical framework for reducing the domain in the mechanical analysis of periodic structures A mathematical framework for reducing the domain in the mechanical analysis of periodic structures

2010-12-14

arxiv.org/abs/1012.3133v2

Physics

Mathematical Physics

18 pages

Scientific paper

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.

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