Synthesis Methods for Lightweight Lattice Structures

Lattice structures are a type of cellular material (e.g., honeycombs, foams, trusses) that can achieve very high stiffness-to-weight and strength-to-weight ratios. When loaded, elements in lattice structures typically stretch and compress, rather than bend, enabling their advantageous performance characteristics. We desire efficient algorithms for searching the large, complex design spaces associated with lattice structure design. In this paper, we present a problem formulation for lattice structure design, using cross-section sizes as variables, and three proposed solution methods. The methods are Particle Swarm Optimization (PSO), Levenburg-Marquardt (LM) algorithm based on a least-squares minimization formulation, and a new non-iterative size matching and scaling method based on results of a finite-element analysis, which are evaluated for their capabilities in achieving light weight and high stiffness. Two-dimensional and 3-D examples are used to test the solution methods.