Optimization of periodic truss materials including constitutive symmetry constraints

Periodic truss materials (PTM) – or Lattice Block Materials (LBM) – belong to the family of the so called ultralight cellular materials, which have attractive engineering properties such as high stiffness/weight ratio and high energy absorption capability. These materials are obtained by the periodic repetition of a unit cell given by a truss structure, so that the orientation of the bars and the cross sectional areas define the material′s macroscopic behavior. In recent years, the development of new process technologies for manufacturing PTMs have brought increased interest in modeling their structural and thermal behavior. In addition to usual analytical and numerical approaches for analyzing the effect of different unit cell configurations on macroscopic properties, optimization techniques have been applied in order to tailor unit cells for achieving desired macroscopic constitutive properties. The present contribution uses mathematical programming for tailoring PTMs through a number of optimization problems in which selected homogenized elastic or thermal constitutive properties are maximized, at the same time that isotropy tries to be enforced by the inclusion of adequate material symmetry constraints. Cross sectional areas and nodal coordinates of the bars are adopted as design variables. 2D examples are presented showing qualitative agreement with results available for 2D elasticity.