Infill topology and shape optimisation of lattice-skin structures

Lattice-skin structures composed of a thin-shell skin and a lattice infill are widespread in nature and large-scale engineering due to their efficiency and exceptional mechanical properties. Recent advances in additive manufacturing, or 3D printing, make it possible to create lattice-skin structures of almost any size with arbitrary shape and geometric complexity. We propose a novel gradient-based approach to optimising both the shape and infill of lattice-skin structures to improve their efficiency further. The respective gradients are computed by fully considering the lattice-skin coupling while the lattice topology and shape optimisation problems are solved in a sequential manner. The shell is modelled as a Kirchhoff-Love shell and analysed using isogeometric subdivision surfaces, whereas the lattice is modelled as a pin-jointed truss. The lattice consists of many cells, possibly of different sizes, with each containing a small number of struts. We propose a penalisation approach akin to the SIMP (solid isotropic material with penalisation) method for topology optimisation of the lattice. Furthermore, a corresponding sensitivity filter and a lattice extraction technique are introduced to ensure the stability of the optimisation process and to eliminate scattered struts of small cross-sectional areas. The developed topology optimisation technique is suitable for non-periodic, non-uniform lattices. For shape optimisation of both the shell and the lattice, the geometry of the lattice-skin structure is parameterised using the free-form deformation technique. The topology and shape optimisation problems are solved in an iterative, sequential manner. The effectiveness of the proposed approach and the influence of different algorithmic parameters are demonstrated with several numerical examples.Comment: 20 pages, 17 figure

Design and Optimization of Functionally-graded Triangular Lattices for Multiple Loading Conditions

Aligning lattices based on local stress distribution is crucial for achieving exceptional structural stiffness. However, this aspect has primarily been investigated under a single load condition, where stress in 2D can be described by two orthogonal principal stress directions. In this paper, we introduce a novel approach for designing and optimizing triangular lattice structures to accommodate multiple loading conditions, which means multiple stress fields. Our method comprises two main steps: homogenization-based topology optimization and geometry-based de-homogenization. To ensure the geometric regularity of triangular lattices, we propose a simplified version of the general rank-$3$ laminate and parameterize the design domain using equilateral triangles with unique thickness per edge. During optimization, the thicknesses and orientation of each equilateral triangle are adjusted based on the homogenized properties of triangular lattices. Our numerical findings demonstrate that this proposed simplification results in only a slight decrease in stiffness, while achieving triangular lattice structures with a compelling geometric regularity. In geometry-based de-homogenization, we adopt a field-aligned triangulation approach to generate a globally consistent triangle mesh, with each triangle oriented according to the optimized orientation field. Our approach for handling multiple loading conditions, akin to de-homogenization techniques for single loading conditions, yields highly detailed, optimized, spatially varying lattice structures. The method is computationally efficient, as simulations and optimizations are conducted at a low-resolution discretization of the design domain. Furthermore, since our approach is geometry-based, obtained structures are encoded into a compact geometric format that facilitates downstream operations such as editing and fabrication

A brick in the wall: Staggered orientable infills for additive manufacturing

International audienceAdditive manufacturing is typically conducted in a layer-by-layer fashion. A key step of the process is to define, within each planar layer, the trajectories along which material is deposited to form the final shape. The direction of these trajectories triggers an anisotropy in the fabricated parts, which directly affects their properties, from their mechanical behavior to their appearance. Controlling this anisotropy paves the way to novel applications, from stronger parts to controlled deformations and surface patterning.This work introduces a method to generate trajectories that precisely follow an input direction field while simultaneously avoiding intra- and inter-layer defects. Our method results in spatially coherent trajectories - all follow the specified direction field throughout the layers - while providing precise control over their inter-layer arrangement. This allows us to generate a staggered layout of trajectories across layers, preventing unavoidable tiny gaps from forming tunnel-shaped voids throughout a part volume.Our approach is simple, robust, easy to implement, and scales linearly with the input volume. It builds upon recent results in procedural generation of oscillating patterns, generating a signal in the 3D domain that oscillates with a frequency matching the deposition beads width while following the input direction field. Trajectories are extracted with a process akin to a marching square