Optmization of a unit periodic cell in lattice block materials aimed at thermo-mechanical applications

Abstract

Lattice block materials (LBMs) are periodic cellular materials, made of truss-like unit cells, which usually present a significant enhancement in mechanical performance when compared to their parent material. This improvement is generally measured by their low weight to strength ratio but several other desirable properties can also be considered, including high capacity for kinetic energy absorption, enhanced vibrational and damping characteristics, acoustic noise attenuation, shear strength, fracture strength, and directional heat conduction or insulation. Using optimization techniques, it is possible to tailor LBMs for specific multifunctional needs, combining good performance in different, and sometimes competing, properties. This work presents a particular approach for a systematic design of unit periodic cells of LBMs aiming at enhanced simultaneous stiffness and heat transfer homogenized properties. The homogenization is developed using an asymptotic expansion in two scales, the unit cells are modeled using linear pin-jointed truss finite elements and the optimization algorithm employed is Sequential Linear Programming (SLP). Nodal coordinates and cross sectional areas might be adopted as design variables simultaneously and the necessary sensitivities are obtained analytically. Illustrative 2D and 3D examples are included.