Optimisation of functionally graded lattice structures using isostatic lines

• Published in: Materials & design Vol. 127; pp. 215 - 223
• Main Authors: Daynes, Stephen, Feih, Stefanie, Lu, Wen Feng, Wei, Jun
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 05.08.2017
• Subjects: Finite element analysis; Functionally graded materials; Lattice structures; Sandwich structures; Topology optimisation; Topology optimisation; Lattice structures; Finite element analysis; Functionally graded materials; Sandwich structures
• ISSN: 0264-1275; 1873-4197
• DOI: 10.1016/j.matdes.2017.04.082

Functionally graded lattice core structures show a gradual and localised variation in their mechanical properties with the aim of improving structural performance whilst minimising weight. We present a novel approach to generate optimised functionally graded lattice core structures. Firstly, topology optimisation is performed to return the optimal core density distribution to minimise the structure's compliance subject to a mass constraint. A series of isostatic lines are then constructed with respect to the local principal stresses to generate a lattice structure spatially graded with respect to lattice cell size, aspect ratio and orientation. To validate this novel approach, optimisation is performed on a sandwich core structure subject to three point bending. Experimental tests confirm the greatly improved stiffness and strength properties (101% and 172% respectively) of the core as a result of spatially grading the lattice cells when compared to a benchmark core with uniform cell size of the same density. The new approach also significantly outperforms lattice structures with graded diameters as optimised by state-of-the-art commercial software packages. Non-dimensional core performance indices are formulated to express the relative specific stiffness and strength properties of the core for the three design approaches. •A novel biomimetic methodology for designing spatially graded lattice structures is presented•Isostatic stress patterns based on the magnitude and direction of principal stresses result in graded lattice spacing•Lattice cells have optimum cell orientation, size and aspect ratio corresponding to external loads•Spatially graded lattices have significantly higher stiffness and strength compared to uniform lattices of the same weight [Display omitted]