A new homogenization scheme for beam and plate structures without a priori requirements on boundary conditions

Abstract This contribution picks up on a novel approach for first order homogenization procedure based the Irving-Kirkwood theory and provides finite element implementation as well applications to beam plate structures. It does not have fundamental problems of dependency from representative volume (RVE) size in determining shear torsional stiffness beams plates, that is present classic Hill-Mandel methods. Due possibility using minimal boundary conditions whilst simultaneously reusing existing algorithms, creation models numerical are much more straight forward. The presented FE formulation limited materially geometrically linear problems. assumption quadratic stress distribution over height (and width case beam), which causes warping cross-section under transverse loading. Results scheme shown various configurations compared values known analytical solutions or computed full scale models.