Multiscale Modelling of Frame Structures With Lattice‐Like Mesostructures Using Finite Beam Elements at the Macro and Meso Level

ABSTRACT

In this contribution, we present a model for shear‐flexible beams with a lattice‐like meso structure. The meso structure consists of a network of beams. The meso ‐ and macroscale are coupled by means of the Hill–Mandel condition. Due to the use of a structural model at the macroscale, the cross‐sectional dimensions of the representative volume element (RVE) are coupled to those of the macroscale beam model. Therefore, we use the term mesoscale instead of microscale. For the first time, we apply periodic boundary conditions to an RVE not only for the translational degrees of freedom, but also for the rotational degrees of freedom. This is done in a way that does not constrain axial strain, shear, torsion, or bending modes. New constraint equations are introduced to prevent rigid‐body translations and rotations, as well as a dependence of the homogenised quantities on the length of the RVE. The proposed method is evaluated using two benchmark tests, which show very good agreement between the numerical results and the reference solution.