Generation and comparison of globally isotropic space-filling truss structures

Abstract

The purposes of this paper are to present a rationale for obtaining space-filling truss structures that behave like a globally isotropic continuum and to use continuum modeling to investigate their relative structural efficiencies (e.g., modulus-to-density, strength-to-density, and part-count-to-volume ratios). The trusses considered herein are generated by replication of a characteristic truss cell uniformly through space. The characteristic cells are categorized by one of a set of possible geometric symmetry groups derived using the techniques of crystallography. The implied elastic symmetry associated with each geometric symmetry group is identified to simplify the task of determining stiffness tailoring rules for guaranteeing global isotropy. Four truss geometries are analyzed to determine stiffness tailoring necessary for isotropy. All geometries exhibit equivalent isotropic Poisson's ratios of 1/4 and equivalent modulus-to-density ratios of 1/6 times the modulus-to-density ratio of the material used in their members. The truss configuration that has the lowest percent difference in member lengths is shown to have the lowest component part-count-to-volume ratios of all geometries considered when compared on a basis of equal stiffness, equal strength, and equal mass.