Design and Optimization of Conforming Lattice Structures

Explicit Topology Optimization of Voronoi Foams

Topology optimization can maximally leverage the high DOFs and mechanical potentiality of porous foams but faces challenges in adapting to free-form outer shapes, maintaining full connectivity between adjacent foam cells, and achieving high simulation accuracy. Utilizing the concept of Voronoi tessellation may help overcome the challenges owing to its distinguished properties on highly flexible topology, natural edge connectivity, and easy shape conforming. However, a variational optimization of the so-called Voronoi foams has not yet been fully explored. In addressing the issue, a concept of explicit topology optimization of open-cell Voronoi foams is proposed that can efficiently and reliably guide the foam's topology and geometry variations under critical physical and geometric requirements. Taking the site (or seed) positions and beam radii as the DOFs, we explore the differentiability of the open-cell Voronoi foams w.r.t. its seed locations, and propose a highly efficient local finite difference method to estimate the derivatives. During the gradient-based optimization, the foam topology can change freely, and some seeds may even be pushed out of shape, which greatly alleviates the challenges of prescribing a fixed underlying grid. The foam's mechanical property is also computed with a much-improved efficiency by an order of magnitude, in comparison with benchmark FEM, via a new material-aware numerical coarsening method on its highly heterogeneous density field counterpart. We show the improved performance of our Voronoi foam in comparison with classical topology optimization approaches and demonstrate its advantages in various settings.

Biologically Inspired Spatial-Temporal Perceiving Strategies for Spiking Neural Network

A future unmanned system needs the ability to perceive, decide and control in an open dynamic environment. In order to fulfill this requirement, it needs to construct a method with a universal environmental perception ability. Moreover, this perceptual process needs to be interpretable and understandable, so that future interactions between unmanned systems and humans can be unimpeded. However, current mainstream DNN (deep learning neural network)-based AI (artificial intelligence) is a 'black box'. We cannot interpret or understand how the decision is made by these AIs. An SNN (spiking neural network), which is more similar to a biological brain than a DNN, has the potential to implement interpretable or understandable AI. In this work, we propose a neuron group-based structural learning method for an SNN to better capture the spatial and temporal information from the external environment, and propose a time-slicing scheme to better interpret the spatial and temporal information of responses generated by an SNN. Results show that our method indeed helps to enhance the environment perception ability of the SNN, and possesses a certain degree of robustness, enhancing the potential to build an interpretable or understandable AI in the future.

Prediction of Mechanical Properties of Lattice Structures: An Application of Artificial Neural Networks Algorithms

The yield strength and Young's modulus of lattice structures are essential mechanical parameters that influence the utilization of materials in the aerospace and medical fields. Currently, accurately determining the Young's modulus and yield strength of lattice structures often requires conduction of a large number of experiments for prediction and validation purposes. To save time and effort to accurately predict the material yield strength and Young's modulus, based on the existing experimental data, finite element analysis is employed to expand the dataset. An artificial neural network algorithm is then used to establish a relationship model between the topology of the lattice structure and Young's modulus (the yield strength), which is analyzed and verified. The Gibson-Ashby model analysis indicates that different lattice structures can be classified into two main deformation forms. To obtain an artificial neural network model that can accurately predict different lattice structures and be deployed in the prediction of BCC-FCC lattice structures, the artificial network model is further optimized and validated. Concurrently, the topology of disparate lattice structures gives rise to a certain discrete form of their dominant deformation, which consequently affects the neural network prediction. In conclusion, the prediction of Young's modulus and yield strength of lattice structures using artificial neural networks is a feasible approach that can contribute to the development of lattice structures in the aerospace and medical fields.

Topology Optimization Via Spatially-Varying TPMS

Structural design with multi-family triply periodic minimal surfaces (TPMS) is a meaningful work that can combine the advantages of different types of TPMS. However, very few methods consider the influence of the blending of different TPMS on structural performance, and the manufacturability of final structure. Therefore, this work proposes a method to design manufacturable microstructures with topology optimization (TO) based on spatially-varying TPMS. In our method, different types of TPMS are simultaneously considered in the optimization to maximize the performance of designed microstructure. The geometric and mechanical properties of the unit cells generated with TPMS, that is minimal surface lattice cell (MSLC), are analyzed to obtain the performance of different types of TPMS. In the designed microstructure, MSLCs of different types are smoothly blended with an interpolation method. To analyze the influence of deformed MSLCs on the performance of the final structure, the blending blocks are introduced to describe the connection cases between different types of MSLCs. The mechanical properties of deformed MSLCs are analyzed and applied in TO process to reduce the influence of deformed MSLCs on the performance of final structure. The infill resolution of MSLC within a given design domain is determined according to the minimal printable wall thickness of MSLC and structural stiffness. Both numerical and physical experimental results demonstrate the effectiveness of the proposed method.

Diatom-inspired stiffness optimization for plates and cellular solids

Diatoms, a class of aquatic autotrophic microorganisms, are characterized by silicified exoskeletons with highly complex architectures. These morphologies have been shaped by the selection pressure that the organisms have been subjected to during their evolutionary history. Two properties which are highly likely to have contributed to the evolutionary success of current diatom species are lightweightness and structural strength. Thousands of diatom species are present in water bodies today, and although each has its unique shell architecture, a strategy that is common across species is the uneven and gradient solid material distribution across their shells. The aim of this study is to present and evaluate two novel structural optimization workflows inspired by material grading strategies in diatoms. The first workflow mimics theAuliscus intermidusdiatoms' surface thickening strategy and generates continuous sheet structures with optimal boundaries and local sheet thickness distributions when applied to plate models subjected to in-plane boundary conditions. The second workflow mimics theTriceratium sp.diatoms' cellular solid grading strategy, and produces 3D cellular solids with optimal boundaries and local parameter distributions. Both methods are evaluated through sample load cases, and prove to be highly efficient in transforming optimization solutions with non-binary relative density distributions into highly performing 3D models.

Stress-field driven conformal lattice design using circle packing algorithm

Reliable extreme lightweight is the pursuit in many high-end manufacturing areas. Aided by additive manufacturing (AM), lattice material has become a promising candidate for lightweight optimization. Configuration of lattice units at the material level and the distribution of lattice units at the structure level are the two main research directions recently. This paper proposes a generative strategy for lattice infilling optimization using organic strut-based lattices. A sphere packing algorithm driven by von Mises stress fields determines the lattice distribution density. Two typical configurations, Voronoi polygons and Delaunay triangles, are adopted to constitute the frames, respectively. Based on finite element analysis, a simplified truss model is utilized to evaluate the lattice distribution in terms of mechanical properties. Optimization parameters, including node number, mapping gradient, and the range of varying circle size, are investigated through the genetic algorithm (GA). Multiple feasible solutions are obtained for further solidification modelling. To avoid the stress concentration, the organic strut-based lattice units are created by the iso-surface modelling method. The effectiveness of the proposed generative approach is illustrated through a classical 3-point bending beam. The stiffness of the optimized structure, verified through experimental testing, has increased 80% over the one using the traditional uniform body center cubic (BCC) lattice distribution.

Wearable 3D Machine Knitting: Automatic Generation of Shaped Knit Sheets to Cover Real-World Objects

Knitting can efficiently fabricate stretchable and durable soft surfaces. These surfaces are often designed to be worn on solid objects as covers, garments, and accessories. Given a 3D model, we consider a knit for it wearable if the knit not only reproduces the shape of the 3D model but also can be put on and taken off from the model without deforming the model. This "wearability" places additional constraints on surface design and fabrication, which existing machine knitting approaches do not take into account. We introduce the first practical automatic pipeline to generate knit designs that are both wearable and machine knittable. Our pipeline handles knittability and wearability with two separate modules that run in parallel. Specifically, given a 3D object and its corresponding 3D garment surface, our approach first converts the garment surface into a topological disc by introducing a set of cuts. The resulting cut surface is then fed into a physically-based unclothing simulation module to ensure the garment's wearability over the object. The unclothing simulation determines which of the previously introduced cuts could be sewn permanently without impacting wearability. Concurrently, the cut surface is converted into an anisotropic stitch mesh. Then, our novel, stochastic, any-time flat-knitting scheduler generates fabrication instructions for an industrial knitting machine. Finally, we fabricate the garment and manually assemble it into one complete covering worn by the target object. We demonstrate our method's robustness and knitting efficiency by fabricating models with various topological and geometric complexities. Further, we show that our method can be incorporated into a knitting design tool for creating knitted garments with customized patterns.

A Hybrid Level Set Method for the Topology Optimization of Functionally Graded Structures

This paper presents a hybrid level set method (HLSM) to design novelty functionally graded structures (FGSs) with complex macroscopic graded patterns. The hybrid level set function (HLSF) is constructed to parametrically model the macro unit cells by introducing the affine concept of convex optimization theory. The global weight coefficients on macro unit cell nodes and the local weight coefficients within the macro unit cell are defined as master and slave design variables, respectively. The local design variables are interpolated by the global design variables to guarantee the C0 continuity of neighboring unit cells. A HLSM-based topology optimization model for the FGSs is established to maximize structural stiffness. The optimization model is solved by the optimality criteria (OC) algorithm. Two typical FGSs design problems are investigated, including thin-walled stiffened structures (TWSSs) and functionally graded cellular structures (FGCSs). In addition, additively manufactured FGCSs with different core layers are tested for bending performance. Numerical examples show that the HLSM is effective for designing FGSs like TWSSs and FGCSs. The bending tests prove that FGSs designed using HLSM are have a high performance.

Scalable, process-oriented beam lattices: generation, characterization, and compensation for open cellular structures

Additively manufactured lattices are emerging as promising candidates for structural, thermal, chemical, and biological applications. However, achieving a satisfactory prototype or final part with this level of complexity requires synthesis of disparate knowledge from the distinctly digital and physical processing stages. This work proposes an integrated framework for processing self-supporting, open lattice structures that do not require supports and facilitate material removal in post-processing steps. We describe a minimal yet comprehensive design strategy for generating uniform lattice structures with conformal open lattice skins for an arbitrary unit cell configuration. Using continuous liquid interface production (CLIP™) on a Carbon M1, printability is evaluated for five unique bending-dominated lattice structures at unit cell length scales from 0.5 - 3.5 mm and strut diameters ranging from 0.11 - 1.05 mm. Using a cubic lattice as a basis, we further examine dimensional fidelity with respect to 2D lattice void dimensions and part position, finding differences between length scales and within parts, due to physical processing artifacts. Finally, we demonstrate a functional grading strategy based on process control methods to compensate for dimensional deviations. Using an iterative approach based on a naïve process model, deviation of the planar strut radius in a cubic lattice was decreased by approximately 85% after two iterations. These insights and strategies can be readily applied to other structures, characterization techniques, and additive manufacturing processes, thereby improving the exchange of information between digital and physical processing and lowering the energy barriers to producing high-quality lattice parts.

Assessing Tetrahedral Lattice Parameters for Engineering Applications Through Finite Element Analysis

Minimizing weight while maintaining strength in components is a continuous struggle within manufacturing industries, especially in aerospace. This study explores how controlling the dimensions of the geometric parameters of a lattice yields ideal mechanical properties for aerospace-related applications. A previously developed Bubble-mesh based computational method was used to generate a novel type of tetrahedral lattice that allows for the manipulation of three geometric parameters: cell size/density, strut diameter, and strut intersection rounding. Topology optimization and lattice generation within components are typical methods used to decrease weight while maintaining strength. Although these are robust optimization methods, each have their faults. Highly topology-optimized components may fail under unexpected loads, and lattice generation within commercial software is often limited in its ability to create ideal lattices with controlled geometric parameters, resulting in lattices with repeating unit cells. In this study, we used finite element methods (FEM)-based compression tests on latticed cubes with various parameter combinations to determine the best balance of lattice parameters. The results showed that strut diameter and strut intersection rounding were the best parameters to control to maintain strength and reduce weight. This understanding of the lattice structures was then applied to two aerospace components: a jet engine bracket and an airplane bearing bracket. By applying tetrahedral lattices with specified strut diameters and strut intersection rounding, the weight of the jet engine bracket was reduced by 51.8%, and the airplane bearing bracket was reduced by 20.5%.

Optimal and continuous multilattice embedding

Because of increased geometric freedom at a widening range of length scales and access to a growing material space, additive manufacturing has spurred renewed interest in topology optimization of parts with spatially varying material properties and structural hierarchy. Simultaneously, a surge of micro/nanoarchitected materials have been demonstrated. Nevertheless, multiscale design and micro/nanoscale additive manufacturing have yet to be sufficiently integrated to achieve free-form, multiscale, biomimetic structures. We unify design and manufacturing of spatially varying, hierarchical structures through a multimicrostructure topology optimization formulation with continuous multimicrostructure embedding. The approach leads to an optimized layout of multiple microstructural materials within an optimized macrostructure geometry, manufactured with continuously graded interfaces. To make the process modular and controllable and to avoid prohibitively expensive surface representations, we embed the microstructures directly into the 3D printer slices. The ideas provide a critical, interdisciplinary link at the convergence of material and structure in optimal design and manufacturing.

FE vibration analyses of novel conforming meta-structures and standard lattices for simple bricks and a topology-optimized aerodynamic bracket

Additive manufacturing (AM) enables production of components that are not possible to make using traditional methods. In particular, lattice-type structures are of recent interest due to their potential for high strength-to-weight ratios and other desirable properties. However, standard periodic lattice structures have problems conforming to complex curved and multi-connected shapes (e.g. holes or sharp-to-smooth mating edges). In addition, standard lattices have well known shear and fatigue weaknesses due to their periodic basis/structure. To address these problems, we developed a new type of shape-conforming meta-structure (HGon) that extends lattices, enabling automated conforming to complex shapes and parametric meta-topology control. HGons also have unique vibration dampening and optimization capabilities. This study presents initial FE analyses of (Part 1) dynamic vibration responses of new HGon meta-structures compared with periodic lattices of equivalent density for a series of basic rectangular structures and (Part 2) a complex multi-connected aerodynamic bracket with field-based stress meta-topology optimization. Results show significantly enhanced vibration dampening behavior and superior strength-to-weight ratios for HGon meta-structures as compared to standard lattices.

Optimal design and manufacture of variable stiffness laminated continuous fiber reinforced composites

Advanced manufacturing methods like multi-material additive manufacturing are enabling realization of multiscale materials with intricate spatially varying microstructures and thus, material properties. This blurs the boundary between material and structure, paving the way to lighter, stiffer, and stronger structures. Taking advantage of these tunable multiscale materials warrants development of novel design methods that effectively marry the concepts of material and structure. We propose such a design to manufacture workflow and demonstrate it with laminated continuous fiber-reinforced composites that possess variable stiffness enabled by spatially varying microstructure. This contrasts with traditional fiber-reinforced composites which typically have a fixed, homogenous microstructure and thus constant stiffness. The proposed workflow includes three steps: (1) Design automation—efficient synthesis of an optimized multiscale design with microstructure homogenization enabling efficiency, (2) Material compilation—interpretation of the homogenized design lacking specificity in microstructural detail to a manufacturable structure, and (3) Digital manufacturing—automated manufacture of the compiled structure. We adapted multiscale topology optimization, a mesh parametrization-based algorithm and voxel-based multimaterial jetting for these three steps, respectively. We demonstrated that our workflow can be applied to arbitrary 2D or 3D surfaces. We validated the complete workflow with experiments on two simple planar structures; the results agree reasonably well with simulations.