Abstract
In this paper we present a numerical investigation into surface-based lattice structures with the aim of facilitating their design for additive manufacturing. We give the surface equations for these structures and show how they can be used to tailor their volume fractions. Finite element analysis is used to investigate the effect of cell type, orientation and volume fraction on the elastic moduli of the lattice structures, giving rise to a valuable set of numerical parameters which can be used to design a lattice to provide a specified stiffness. We find the I-WP lattice in the [001] orientation provides the highest stiffness along a single loading direction, but the diamond lattice may be more suitable for cases where lower mechanical anisotropy is important. Our stiffness models enable the construction of a powerful numerical tool for predicting the performance of graded structures. We highlight a particular problem which can arise when two lattice types are hybridised; an aberration leading to structural weakening and high stress concentrations. We put forward a novel solution to this problem and demonstrate its usage. The methods and results detailed in this paper enable the efficient design of lattice structures functionally graded by volume fraction and cell type.
Highlights
We extend our elastic moduli analysis to include different lattice orientations and volume fractions
We lay out our findings concerning lattice functional grading, where the volume fraction and cell type are varied throughout the structure
We demonstrate how the Gibson-Ashby scaling laws can be used to approximate the stiffness of arbitrarily graded lattices structures, and we highlight one approach to the problem of reduced strut thickness that can arise when one cell type transitions into another
Summary
Lattices are seen as a potential replacement for solid volumes, providing benefits such as weightreduction and decreased part production time Other properties of these structures that have attracted attention are their energy absorption under compressive and dynamic loading [1,2,3,4,5], their facility to act as heat exchangers [6,7], their applications in orthopaedic implants [8] and their potential to reduce noise and vibration transmission [9,10,11].
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