This paper compares the representative volume element (RVE)
method based on Dirichlet and Neumann boundary conditions
with the homogenization method for predicting the effective
elastic property of truss material with periodic
microstructure. Numerical experiments show that, with
increase of the number of the unit cell, n, the results of
RVE method under the Dirichlet and Neumann boundary
conditions converge towards those obtained with
homogenization method from the above and below sides,
respectively. For RVE method, a simple criterion for
judging the existence of scale effects is whether the
equilibrium of the boundary nodal forces is guaranteed
under the Dirichlet boundary conditions, or whether the
deformation compatibility at the unit cell boundaries is
satisfied under the Neumann boundary conditions. We also
discover that for a specific type of truss material, whose
unit cell has no characteristic displacement defined in
homogenization method, the volume average of members’
properties in the unit cell gives the exact prediction of
the effective elastic properties. Finally, shape
optimization technique is applied to find the optimal
geometric shape of the unit cell for truss material with
the maximum and minimum shear stiffness, and the numerical
singularity involved is discussed as well.