On Periodic Boundary Conditions in Variationally Consistent Homogenisation of Beams and Plates

A computationally efficient strategy to prescribe periodic boundary conditions on three- dimensional Representative Volume Elements (RVEs) is outlined. In particular, the cases of having an Euler-Bernoulli beam and a Kirchhff-Love plate problem at the macroscale are considered within a computational homogenisation framework. Special solid elements for the boundary region of the periodic mesh have been developed, in which some of the degrees of freedom depend on those of their periodic counterparts, the macroscopic data and the size of the RVE.