Effective constitutive relations for the microstructure of periodic frames

Abstract

Effective micro-structure properties of two-dimensional large repetitive frame-like structures are derived using straightforward combinations of energy methods of linear transformations. Once the actual structure is identified symmetry considerations are used in order to identify its independent property constants. The actual values of these constants are constructed according to a building block format which is carried out in the three consecutive steps: (1) all basic planar lattices are identified, (2) effective continuum properties are derived for each of these planar basic grids using energy methods, and (3) orthogonal transformations are finally used to determine the contribution of each basic set to the overall effective continuum properties of the structure.