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 anEuler-Bernoulli beam and a Kirchhoff-Love plate problem at the macroscale are considered within acomputational homogenisation framework. Special solid elements for the boundary region of the periodicmesh have been developed, in which some of the degrees of freedom depend on those of their periodiccounterparts, the macroscopic data and the size of the RVE