Optimization Of Lattice Structures Research Articles

Effects of design and manufacturing deviations on compressive properties of glass sponge lattice structures manufactured by selective laser melting

Bio-inspiration offers researchers innovative perspectives and methodologies, stimulating the advancement of high-performance, high-durability, and added-value materials, structures, and products. Inspired by the lightweight, high-strength, and highly stable glass sponges (GSs), five types of glass sponge lattice structures (GSLSs) were successfully designed and manufactured by selective laser melting (SLM) with Ti6Al4V. By conducting a comparative analysis of unit cell design and manufacturing deviations, we assess their impact on the compressive properties of GSLSs. Notably, the original GSLS with circle-/grid-like heterogeneous geometries exhibits outstanding overall compression performance, including stability, stress dispersion and unique cell-by-cell and layer-by-layer fracture mechanisms among GSLSs, which are attributable to their reinforced diagonal struts and heterogeneous unit cells. Hence, three strategies for unit cell design and optimization were proposed. These discoveries guide the future design and optimization of lattice structures (LSs) and offer potential applications for GSLSs in aerospace, biomedicine, automobiles, architecture, and wearable products.

Design Optimization of Lattice Structures Under Impact Loading for Additive Manufacturing

Abstract Additive manufacturing (AM) has enabled the production of intricate lattice structures with excellent performance and minimal mass. Design approaches that consider static loading, including lattice-based topology optimization (TO), have been well-researched recently. However, to date, there appears to be no widely accepted method of optimizing lattice structures for high-strain rate loading, especially when the design for additive manufacturing (DFAM) principles are considered. This study proposes a computational framework for the design of lattice structures under specified impact loading. To manage dimensionality while achieving sufficient generality, a heuristic design space is developed that relies on traditional TO to govern the design's macrostructure and standard dimensioning to govern its mesostructure. DFAM principles are then incorporated into a Bayesian optimization scheme wrapped around traditional TO to achieve manufacturable designs that absorb high-impact loading. Because this approach does not require analytical gradient information, the framework can be used to optimize directly on complex objectives, such as injury metrics calculated from the acceleration curve. A series of case studies is formulated around a mass-performance tradeoff and involves individual unit cell design as well as full-part design. The proposed design parameterization is found to enable sufficient flexibility to achieve consistently good performance regardless of AM build orientation.

Structural and thermal properties of H6Ta2O17

The structural, electronic, mechanical, and thermal properties of H6Ta2O17 are studied using density functional theory. The Helmholtz free energy is computed for various symmetry constraints on the H6Ta2O17 structure during lattice structure optimization and atomic configuration relax- ation. The Helmholtz free energies calculated from Γ-point phonon frequencies demonstrate a pref- erence for slightly lowered symmetry, preferring triclinic symmetry rather than the experimentally determined orthorhombic symmetry. Elastic constants are obtained for the symmetry-enforced (i.e., orthorhombic) structure and are used to calculate the structure’s mechanical and thermal properties including its bulk, shear, and Young’s moduli, Poisson ratio, Pugh ratio, longitudinal and shear sound velocities, and Debye temperature. Using the Born criteria, the symmetry-enforced structure is shown to be mechanically stable. The electronic band structure for H6Ta2O17 is pre- sented and found to exhibit a large indirect band gap.

Multiscale topology optimization for solid–lattice–void hybrid structures through an ordered multi-phase interpolation

In this paper, we propose a new multiscale topology optimization method to design the solid-lattice-void hybrid structures. A novel ordered solid-lattice-void interpolation model has been developed that realizes smooth transition across the solid, lattice, and void phases, and very importantly, this interpolation model coordinates well between the multiple variables describing the lattice configuration and the relative density variable indicating the solid, lattice, or void status. Specifically, a multi-variable lattice resulted from topology optimization is accepted as the candidate lattice and its effective elastic properties are established through regressive fitting. Then, the ordered solid-lattice-void interpolation formula is developed, which unifies the multi-phase interpolation that allows exceeding the lattice upper/lower limit to reach the solid/void status for the elements. Finally, the multiscale topology optimization algorithm is formulated and implemented for solid-lattice-void hybrid structure design. Numerical examples are studied which demonstrate significant structural performance improvement compared with pure lattice-infilled structures. Finally, additive manufacturing and mechanical tests are conducted to validate the effectiveness of the proposed method. • Propose a new multiscale topology optimization method to design the solid-lattice-void hybrid structures. • Develop a novel ordered solid-lattice-void interpolation model that realizes smooth transition across the solid, lattice, and void phases. • Develop a multi-variable lattice resulted from topology optimization as the candidate lattice. • Demonstrate significant performance improvement by involving the solid and void phases in lattice structure optimization.

Design, mechanical properties and optimization of lattice structures with hollow prismatic struts

Lattice structures with hollow struts exhibit superior mechanical properties as compared to solid ones. In this study, we introduce a new type of body-centered cubic (BCC) lattice, consisting of hollow prismatic struts with mechanical properties defined by an inner hollow parameter. The mechanical properties and deformation behavior of the BCC lattice structures with different inner hollow parameters are investigated under periodic boundary conditions. It is shown that the elastic modulus of the hollow-strut BCC lattice structure improves significantly by 598%-1460% and their deformation mechanism gradually changes from bending-dominated to stretching-dominated, when the inner hollow size increases. In contrast, there are little influences on shear deformation. Interestingly, tunable Poisson's ratio and isotropic elasticity can be achieved by adjusting the inner hollow size. In addition, the BCC lattice structures with different inner hollow parameters are fabricated by digital light processing for compression tests, and the experimental results are in good agreement with the simulation with relative errors of less than 14.6%. Finally, a high-fidelity interpolation model is employed to describe the effective elastic matrix of lattice structures, and a new optimization framework is proposed to simultaneously optimize the distribution of the volume fraction and inner hollow size of hollow-strut lattice structures. This proposed approach significantly improves the stiffness (compliance decreased by 15.8% to 53.1%) of the cantilever beam as compared to traditional optimal designs, demonstrating the potential application of the proposed approach in lightweight designs.

Development and optimization of lattice structure on the walnut shell reinforced PLA composite for the tensile strength and dimensional error properties

The organic fillers and honeycomb lattice structure intruded novel bio-composite materials for the 3D printing application is a practical and eco-friendly approach for developing lightweight biopolymeric components. The present work investigates the impact of incorporation of hexagon lattice structure on the walnut shell/PLA polymeric composite material using the Fused Deposition Modelling method. The printing process parameters such as nozzle temperature, layer height, infill density, and printing speed are varied to optimize the tensile and dimensional area error properties. Taguchi optimization technique is employed to find the optimal printing condition for the effective experimental output responses. The results from the experiments clearly show that the maximum tensile strength of 2.684 MPa was observed on the optimized printing condition of nozzle temperature of 210℃, a layer height of 0.1 mm, an infill density of 100 %, and a printing speed of 20 mm/sec. The developed mathematical model from the regression analysis depicted the R-square value concerning the output responses like tensile strength will be 92.24, and dimensional area error will be 87.48. It proclaims that; the model is fit for the large-scale production of the hexagon lattice structure in the walnut shell/PLA composite. Furthermore, the macrographs of the tested composites fabricated at higher infill density exhibited lower sidewall edge failure than the samples fabricated at the lowest infill density percentages.

The parametrized superelement approach for lattice joint modelling and simulation

From large scale structures such as bridges and cranes to small-scale structures such as lattices, mechanical structures today increasingly consist of “tuneable parts”: parts with a simple geometry described by a small set of strongly varying parameters. For example, although a bridge is a macroscale structure with a complex geometry, it is made from simple beams, bolts and plates, all of which depend on spatially varying, geometrical parameters such as their length-to-width ratio. Accelerating this trend is the concurrent improvement of, on one hand, Additive Manufacturing techniques that allow for increasingly complex parts to be manufactured and, on the other, structural optimization techniques that exploit this expanded design space. However, this trend also poses a challenge to current simulation techniques, as for example the Finite Element Method requires large amounts of elements to represent such structures. We propose to exploit the large conformity between parts inside the mechanical structure through construction of semi-analytic “Parametrized Superelements”, built by meshing with solid elements, reduction to a fixed interface and approximation of the reduced stiffness matrices. These new elements can be employed next to standard elements, enabling the simulation of more complex geometries. The technique we propose is applied to lattice structures and provides a flexible, differentiable, more accurate but still efficient way to simulate their elastic response. A net gain in total computation time occurs after simulating more than twenty lattices. As such, the proposed method enables large-scale parameter exploration and optimization of lattice structures for improved energy absorption, mass and/or stiffness.

Multi-scale collaborative optimization of lattice structures using laser additive manufacturing

In the present work, an effective and efficient design approach is proposed to obtain a three-dimensional multi-scale graded lattice structure by virtue of multiple control parameters via density-based topology optimization. To balance the computational accuracy and cost, a Parameterized Interpolation of Lattice Structure (PILS) model was established, and the math formula combined two novel designing parameters: relative density at macro-scale and aspect ratio at micro-scale. A multinomial function was employed to describe the explicit association between control parameters and equivalent elastic constants with regard to relative density and aspect ratio, which avoided tedious homogenization computation burden in the structural optimization process. Consequently, the multi-scale collaborative design approach could optimize the macro material density distribution and the micro cell topology in an integrated manner. Numerical examples with respect to compliance optimization were offered to validate the benefits of the proposed approach. Finally, the quasi-static and dynamic compression tests were respectively implemented by universal testing machine and Split Hopkinson Pressure Bar (SHPB) system on lattice structures manufactured by laser powder bed fusion (LPBF). The outcomes reveal that graded lattice structures exhibit remarkably improved load-bearing performance than the uniform lattice structures.

Hybrid swarm-based intelligent algorithm for lattice structure optimization in additive manufacturing system

Hybrid swarm-based intelligent algorithm for lattice structure optimization in additive manufacturing system

Multi-scale and multi-material topology optimization of gradient lattice structures using surrogate models

Lattice structures have received considerable attention in the recent years due to the increasingly high flexibility and resolution offered by additive manufacturing techniques. They also present an attractive design approach for applications such as aerospace and biomedical engineering due to their desirable properties including lightweight, high specific strength and stiffness and heat dissipation. This work explores a computationally efficient topology optimization approach while increasing the flexibility of a restricted unit cell design. Unrestricted material unit cell designs are often associated with high computational power and connectivity problems, while highly restricted lattice unit cell designs may lack the potential to reach the optimal desired properties at a reduced computational effort. A two-scale concurrent optimization of lattice structure is proposed in this study, where the topology optimization at the macro-scale structure and the underlying material micro-structures is performed simultaneously to achieve optimal topologies. Surrogate models are used to represent material and geometrical properties for a continuous topology optimization approach. An energy-based homogenization method combined with voxelization is employed to obtain the elasticity tensors for a lattice unit cell library. A multi-variable parameterization of the material unit cell is defined, which allows for the synthesis of functionally graded lattice structures. A multi-material extension to the concurrent multi-scale topology optimization is also explored. The performance of the optimized graded lattice structure is compared to a uniform lattice structure.

Design Optimization of Lattice Structures under Compression: Study of Unit Cell Types and Cell Arrangements.

Additive manufacturing enables innovative structural design for industrial applications, which allows the fabrication of lattice structures with enhanced mechanical properties, including a high strength-to-relative-density ratio. However, to commercialize lattice structures, it is necessary to define the designability of lattice geometries and characterize the associated mechanical responses, including the compressive strength. The objective of this study was to provide an optimized design process for lattice structures and develop a lattice structure characterization database that can be used to differentiate unit cell topologies and guide the unit cell selection for compression-dominated structures. Linear static finite element analysis (FEA), nonlinear FEA, and experimental tests were performed on 11 types of unit cell-based lattice structures with dimensions of 20 mm × 20 mm × 20 mm. Consequently, under the same relative density conditions, simple cubic, octahedron, truncated cube, and truncated octahedron-based lattice structures with a 3 × 3 × 3 array pattern showed the best axial compressive strength properties. Correlations among the unit cell types, lattice structure topologies, relative densities, unit cell array patterns, and mechanical properties were identified, indicating their influence in describing and predicting the behaviors of lattice structures.

Combining Macro- and Mesoscale Optimization: A Case Study of the General Electric Jet Engine Bracket

Topology optimization (TO) is a mathematical method that optimizes the material layout in a pre-defined design domain. Its theoretical background is widely known for macro-, meso-, and microscale levels of a structure. The macroscale TO is now available in the majority of commercial TO software, while only a few software packages offer a mesoscale TO with the design and optimization of lattice structures. However, they still lack a practical simultaneous macro–mesoscale TO. It is not clear to the designers how they can combine and apply TO at different levels. In this paper, a two-scale TO is conducted using the homogenization theory at both the macro- and mesoscale structural levels. In this way, the benefits of the existence and optimization of mesoscale structures were researched. For this reason, as a case study, a commercial example of the known jet engine bracket from General Electric (GE bracket) was used. Different optimization workflows were implemented in order to develop alternative design concepts of the same mass. The design concepts were compared with respect to their weight, strength, and simulation time for the given load cases. In addition, the lightest design concept among them was identified.

ラティス体積分率分布最適化と金属積層造形による傾斜機能構造体の温度分布設計

In recent years, additive manufacturing (AM) has been used in industrial products for fabricating complex geometry. On the other hand, topological optimization is a suitable method for designing complex geometry. Therefore, there are many studies of combining AM and topological optimization these days. As a variant of topological optimization, density optimization of lattice structure is recently studied. The lattice structure is a characteristic one that includes void inside structure fabricated by AM. The designed model by topological optimization should be modified for a suitable structure for AM process. This research tried to use lattice volume fraction optimization for an industrial AM product. Firstly, we have developed a method of designing the lattice unit cell that its effective thermal conductivity is controlled by design variables. Effective thermal conductivity of lattice is calculated by homogenization method and finite element method (FEM). It was confirmed that the effective thermal conductivity changes depending on the size of the internal pores. Next, we consider the minimization problem of the surface temperature of the target domain. By lattice volume fraction optimization, the uniformity of the surface temperature of the target domain was improved. In addition, we fabricated test pieces of lattice and 3D example model by using selective laser melting additive manufacturing. The results showed that the error between the measurement and the analysis using the test piece was sufficiently small.

Integration of Design for Additive Manufacturing Constraints With Multimaterial Topology Optimization of Lattice Structures for Optimized Thermal and Mechanical Properties

Abstract The design of multimaterial lattice structures with optimized elasticity tensor, coefficient of thermal expansion (CTE), and thermal conductivity is the main objective of the research presented in this article. In addition, the additive manufacturability of the lattice structure is addressed using a prismatic density filter to eliminate support structures, and an octant symmetry filter is used to design symmetric lattices. A density-based topology optimization model is formulated with a homogenization method and solved using a sequential linear programming method to obtain the desired unit cell geometry of the lattice structure. The optimized unit cell obtained has high mechanical stiffness, a low CTE, and low thermal conductivity. A finite element analysis is carried out on the optimized lattice structure and an equivalent cube of computed effective properties (with the same loading and boundary conditions) to validate the computed homogenized material properties. The results from the finite element analysis show that the methodology followed to generate the lattice structure is accurate. Such lattice structures with tailored material properties can be used in aerospace parts that are subjected to mechanical and thermal loads. The complex multimaterial geometry produced from the topology optimization routine presented here is intended explicitly for the manufacture of parts using the directed energy deposition process with multiple material deposition nozzles.

Design optimization of lattice structures with stress constraints

This paper presents an experimentally validated framework used to perform topology and orientation (morphology) optimization of lattice structures subject to stress constraints. The effective stiffnesses and yield stresses of a unit cell are obtained using numerical homogenization and validated experimentally. Due to the orthotropic behavior of the unit cell, the modified Hill’s yield criterion is used to describe the lattice strength. The effective orthotropic properties are implemented via macrostructure topology optimization to further improve the lattice structure stiffness. Homogenization-based optimization is performed using a coarse mesh and the optimized design is projected onto a fine mesh. This reduces the computational cost significantly. Finally, the projected design is post-processed to ensure the fabrication feasibility of the optimized lattice structure. The framework is tested for two cases: an L-shaped bracket and a single-edge notched bend (SENB) problem. A comparison of the compliance-based and stress-constrained designs used in the two cases demonstrates that the changes in the optimal material distribution that occur upon implementing the stress constraint result in higher yield strength. The SENB lattice structures are additively manufactured and the stiffnesses and yield strength of the optimized designs are compared to those obtained numerically.

Temperature Distribution Design Based on Variable Lattice Density Optimization and Metal Additive Manufacturing

Additive manufacturing (AM) is employed for fabricating industrial products with complex geometries. As topological optimization is suitable for designing complex geometries, studies have combined AM and topological optimization, evaluating the density optimization of lattice structures as a variant of topological optimization. The lattice structures of components fabricated via AM comprise voids. Models designed using topological optimization should be modified to ensure structures suitable for AM. As the lattice unit can be easily fabricated using AM with fewer design modifications, this study uses lattice density optimization for an industrial AM product. We propose a method of optimizing the lattice distribution for controlling the surface temperature uniformity of industrial products, such as molds. The effective thermal conductivity of the lattice is calculated using the homogenization and finite element methods. The effective thermal conductivity changes depending on the internal pore sizes. The proposed methodology is validated using a 3D example; the minimization problem of surface temperature variations in the target domain is considered. The variable density of the embedded lattice in the target domain is optimized, and we experimentally validated the performance of the lattice unit cell and optimal 3D structure using metal powder bed fusion AM.

Application of Laser-Based Powder Bed Fusion for Direct Metal Tooling

The journey of production tools in cold working, hot working, and injection molding from rapid tooling to additive manufacturing (AM) by laser-based powder bed fusion (L-PBF) is described. The current machines and their configurations, tool steel powder materials and their properties, and the L-PBF process parameters for these materials are specified. Examples of production tools designed for and made by L-PBF are described. Efficient design, i.e., high tooling efficiency and performance in operation, should be the primary target in tool design. Topology and lattice structure optimization provide additional benefits. Using efficient design, L-PBF exhibits the greatest potential for tooling in hot working and injection molding. L-PBF yields high tooling costs, but competitive total costs in hot working and injection molding. Larger object sizes that can be made by L-PBF, a larger number of powder metals that are designed for different tooling applications, lower feedstock and L-PBF processing costs, further L-PBF productivity improvement, improved surface roughness through L-PBF, and secured quality are some of the targets for the research and development in the future. A system view, e.g., plants with a high degree of automation and eventually with cyber-physically controlled smart L-PBF inclusive manufacturing systems, is also of great significance.

An experimental investigation of analytical vs. numerical lattice structure design tools

Recent advances in additive manufacturing technologies have simplified the implementation of lattice structures for different applications. Consequently, FEA packages are moving in the direction of incorporating lattice structure optimization as standard design tools. In this work, we evaluate two lattice structure design methodologies; a continuum-based analytical model vs. a numerical technique implemented in Altair HyperWorks. Comparison samples are verified using FEA and further validated using 3D printing and mechanical testing. FEA results showed comparable performance of the analytical vs. numerical models, but experimental validation showed some discrepancies attributed to the manufacturing method rather than the design process itself.

Topology optimization of lattice structure on a brake pedal

Additive manufacturing technologies can subdue the constraints of conventional manufacturing methods in the fabrication of highly complex lattice structures. Lattice structures have received particular attention in applications where material and weight reduction are significant. The research presented in this paper focuses on the weight reduction of a brake pedal utilizing lattice structures. Lattice structures are generated on the brake pedal replacing the material region followed by the topology optimization of the lattice structure for a given force acting on it. The results show that displacement and stress for the solid and optimized parts are comparable with a 21.2% reduction in mass.

Design and Optimization of Lattice Structures: A Review

Cellular structures consist of foams, honeycombs, and lattices. Lattices have many outstanding properties over foams and honeycombs, such as lightweight, high strength, absorbing energy, and reducing vibration, which has been extensively studied and concerned. Because of excellent properties, lattice structures have been widely used in aviation, bio-engineering, automation, and other industrial fields. In particular, the application of additive manufacturing (AM) technology used for fabricating lattice structures has pushed the development of designing lattice structures to a new stage and made a breakthrough progress. By searching a large number of research literature, the primary work of this paper reviews the lattice structures. First, based on the introductions about lattices of literature, the definition and classification of lattice structures are concluded. Lattice structures are divided into two general categories in this paper: uniform and non-uniform. Second, the performance and application of lattice structures are introduced in detail. In addition, the fabricating methods of lattice structures, i.e., traditional processing and additive manufacturing, are evaluated. Third, for uniform lattice structures, the main concern during design is to develop highly functional unit cells, which in this paper is summarized as three different methods, i.e., geometric unit cell based, mathematical algorithm generated, and topology optimization. Forth, non-uniform lattice structures are reviewed from two aspects of gradient and topology optimization. These methods include Voronoi-tessellation, size gradient method (SGM), size matching and scaling (SMS), and homogenization, optimization, and construction (HOC). Finally, the future development of lattice structures is prospected from different aspects.