The use of central reflection in the formulation of unit cells for micromechanical FEA

Central reflection as a type of symmetry has been exploited in the context of structural analysis for the first time in this paper, especially in terms of applications to the formulation of unit cells for micromechanical FE analysis of materials of periodic microstructures. It reduces the size of the unit cell to be analysed without compromising useful features of the unit cells obtained purely from periodic conditions, viz. the unit cell can still be analysed with a single set of boundary conditions under all loading conditions and any combined loading condition. Such a feature cannot be preserved if a conventional plane reflectional symmetry or a rotational symmetry has been used in order to reduce the size of the unit cell to be analysed. Most of existing unit cells obtained purely from periodic conditions can benefit from this further symmetry. Boundary conditions for unit cells of reduced sizes resulting from the use of the centrally reflectional symmetry have been derived rationally in this paper. They have been validated systematically through examples of applications.