Programmed-Lattice Editor and accelerated processing of parametric program-representations of steady lattices

Abstract

Our goal is to facilitate the design, analysis, optimization, and additive manufacturing of a specific class of 3D lattices that may comprise an extremely large number of elements. We target lattices that exhibit periodicity and uniform geometric gradations in three directions, along possibly curved axes. We propose a Parametric Program-Representation (PPR) of periodic lattices, wherein we represent a lattice by a program with a selected set of exposed control parameters that may be used to adjust the overall shape of the lattice, its repetition count in each direction, its microstructure, and its gradation. In our Programmed-Lattice Editor (PLE), a typical lattice is represented by a short program of 10 to 50 statements. We propose a simple API and a few rudimentary GUI tools that automate the creation of the corresponding expressions in the program. The overall shape and gradation of the lattice is controlled by three similarity transformations. This deliberate design choice ensures that the gradation in each direction is regular (i.e., mathematically steady), that each cell can be evaluated directly, without iterations, and that integral properties (such as surface area, volume, center of mass and spherical inertia of the whole lattice) can be obtained rapidly without having to calculate them for each individual element of the lattice.