Optimal mechanical design of tetrahedral truss cores for sandwich constructions

Lattice truss cores are an emerging family of synthetic periodic materials that can add multifunctional capabilities to lightweight sandwich constructions while maintaining high standards of strength and stiffness. Recent strides in prototyping technologies allow efficient monolithic truss cores to be built from advanced metals without the nuisances of assembled constructions. Based on published models for these materials, this paper tackles the optimal design of tetrahedral truss cores for minimum density under prescribed constraints on strength and stiffness. A closed-form, single-pass algorithm is developed, which finds the optimum after a finite number of steps. The method shows that the best tetrahedral truss core depends on the initial conditions, though 45 degrees orientations are most likely to occur and squatter shapes are rarely convenient. A numerical example demonstrates that optimized aluminium tetrahedral cores outperform high-profile polymer foams and compete favourably with commercial-grade aluminium honeycombs of equal density. The general approach disclosed can be applied to the mechanical optimization of other types of truss core (e.g. pyramidal or kagome, single- or multilayered) and classical periodic design (e.g. corrugated cores), which so far have been analyzed in a less general way.