Optimization Of Lattice Structures Research Articles

Lattice structure design optimization coupling anisotropy and constraints of additive manufacturing

Replacing solid structures with lattice structure is a way enabled by additive manufacturing (AM) to realize part lightweight design. Conventional design optimization method based on homogeneous periodic lattice structure cannot achieve the optimal structure without taking the stress magnitude and orientation into account. A design optimization method of heterogeneous conformal lattice structure coupling constraints and anisotropy of AM based on principal stress lines (PSL) is proposed. (1) The PSL is calculated based on finite element analysis to visualize the path of load transfer. (2) The load-adapted lattice structure is generated guided by the PSL. (3) In order to further optimize lattice structure, the lattice structure optimization model is established by coupling anisotropy and constraints of AM based on the fused deposition modeling (FDM) experiment. Taking a cantilever beam as a case, the maximum force-to-weight ratio and the stiffness-to-weight ratio of the optimized heterogeneous conformal lattice structure are increased by 11.8% and 41.8% respectively compared with homogeneous conformal lattice structure, which verified the feasibility of the proposed method.

Clustering-based multiscale topology optimization of thermo-elastic lattice structures

A multiscale clustering-based topology optimization for thermo-elastic lattice structures is studied based on the extended multiscale finite element method (EMsFEM). The strain energy of thermo-elastic lattice structures is chosen as the objective function. The microstructural configuration and the macrostructural distribution of the thermo-elastic lattice material are designed through topology optimization concurrently. The K-means clustering-based method is proposed to group the microstructures of the lattice materials. The effects of the number of clusters (groups), magnitude of the thermal loads, size factor of the microstructure, and material volume fraction on the optimization results are discussed. The results show that the clustering-based multiscale design optimization is superior to the classical multiscale design optimization of lattice structures.

Lattice structure optimization and homogenization through finite element analyses

Lattice topology optimization can stimulate the design of new materials with spatially dependent properties with composite parts or three-dimensional printed components. The present work considers a mounting bracket for an industrial robotic arm as a case study, having as the main objective the increase of the fundamental frequency and secondly its mass reduction. Two design approaches were considered by using the ANSYS software: the first stage optimized the orthotropic lattice material by establishing an optimal variable cubic cell lattice density distribution in the geometric model; the second stage used a homogenized model based on the lattice optimization resulted from the previous stage and considered different volume fractions and variable density for four different types of cells. Homogenization increased the stiffness of the bracket by using the same cubic lattice cell and the fundamental frequency increased from 1227 Hz obtained with lattice optimization to 1366 Hz after homogenization. For the unoptimized bracket the fundamental frequency was only 839 Hz. The mass was reduced to more than half. The most effective proved to be the midpoint lattice cell as by homogenization the mass was reduced from 45.5 kg to 18.22 kg.

Two-scale concurrent topology optimization of lattice structures with connectable microstructures

Two-scale concurrent design of lattice material microstructures and their macroscale distributions can effectively enlarge the design space, and thus achieve lightweight structures with desirable mechanical and multi-physics performances. Most of the existing inverse homogenization-based design methods do not take into consideration the connectivity issues of the microstructures. In practice, this may hinder the manufacturing and application of the optimized two-scale designs. To handle this issue, the present paper proposes a designable connective region method to obtain connectable microstructures in the context of two-scale concurrent structural topology optimization, considering structures composed of lattice materials with repetitive unit cells and prescribed porosity. On the microscale, the microstructures topologies are represented by the density model, and the effective material properties are computed with the homogenization method. On the macroscale, the distribution of different lattice materials is described with the discrete material optimization method, which can effectively reduce the amounts of macroscale elements with intermediate densities. The connectivity between any two types of the microstructures is naturally ensured by introducing pre-defined connective regions in the microstructural unit cells and keeping these regions sharing the same topology. This method can be conveniently implemented through microscale design variable linking and requires no evaluation of extra connectivity constraints and the corresponding sensitivities. It is exemplified by two-scale concurrent structural topology optimization for compliance minimization problems in two- and three-dimensional design domains. Numerical results show that this method is able to generate connectable lattice structures, which exhibits improved stiffness as compared with their uniform-lattice counterparts.

Optimum design of automobile components using lattice structures for additive manufacturing

Abstract In today’s world, reducing fuel consumption is one of the most important goals for the automotive industry. For this reason, weight reduction is one of the main topics in this research and for various companies. In this research, topology optimization was conducted on a suspension arm as a means of ensuring balance in automobiles. Subsequently, the model, formed by topology optimization was filled with a lattice structure and re-optimized by size optimization to obtain optimum dimensions for the model. These operations are described as lattice structure optimization. Additive manufacturing (3D printer) is necessary to produce complex models (after topology and lattice structure optimization). A static analysis of the new models was conducted by using the finite element method, and the results were compared with those of the initial design of the model. As a result of the comparison, positive results were obtained, and it was shown that topology optimization and lattice structural optimization could be used in the design of vehicle elements. According to the results obtained from lattice structure optimization, design structure can be formed more reliably than via topology optimization. In addition, both configurations and layouts of the cellular structures have a special effect on the overall performance of the lattice structure.

Optimum design of automobile components using lattice structures for additive manufacturing

Abstract In today’s world, reducing fuel consumption is one of the most important goals for the automotive industry. For this reason, weight reduction is one of the main topics in this research and for various companies. In this research, topology optimization was conducted on a suspension arm as a means of ensuring balance in automobiles. Subsequently, the model, formed by topology optimization was filled with a lattice structure and re-optimized by size optimization to obtain optimum dimensions for the model. These operations are described as lattice structure optimization. Additive manufacturing (3D printer) is necessary to produce complex models (after topology and lattice structure optimization). A static analysis of the new models was conducted by using the finite element method, and the results were compared with those of the initial design of the model. As a result of the comparison, positive results were obtained, and it was shown that topology optimization and lattice structural optimization could be used in the design of vehicle elements. According to the results obtained from lattice structure optimization, design structure can be formed more reliably than via topology optimization. In addition, both configurations and layouts of the cellular structures have a special effect on the overall performance of the lattice structure.

Multi-material topology optimization of lattice structures using geometry projection

This work presents a computational method for the design of architected truss lattice materials where each strut can be made of one of a set of available materials. We design the lattices to extremize effective properties. As customary in topology optimization, we design a periodic unit cell of the lattice and obtain the effective properties via numerical homogenization. Each bar is represented as a cylindrical offset surface of a medial axis parameterized by the positions of the endpoints of the medial axis. These parameters are smoothly mapped onto a continuous density field for the primal and sensitivity analysis via the geometry projection method. A size variable per material is ascribed to each bar and penalized as in density-based topology optimization to facilitate the entire removal of bars from the design. During the optimization, we allow bars to be made of a mixture of the available materials. However, to ensure each bar is either exclusively made of one material or removed altogether from the optimal design, we impose optimization constraints that ensure each size variable is 0 or 1, and that at most one material size variable is 1. The proposed material interpolation scheme readily accommodates any number of materials. To obtain lattices with desired material symmetries, we design only a reference region of the unit cell and reflect its geometry projection with respect to the appropriate planes of symmetry. Also, to ensure bars remain whole upon reflection inside the unit cell or with respect to the periodic boundaries, we impose a no-cut constraint on the bars. We demonstrate the efficacy of our method via numerical examples of bulk and shear moduli maximization and Poisson’s ratio minimization for two- and three-material lattices with cubic symmetry.

Multi-objective crashworthiness optimization of lattice structure filled thin-walled tubes

Abstract Thin-walled tubes have been mostly used in passive vehicle safety systems as crash energy absorber. With the use of additive manufacturing technology, it is possible to produce novel filler materials to further enhance the crashworthiness performance of thin-walled tubes. In this study, optimal designs of novel lattice structure filled square thin-walled tubes are investigated under axial impact loading by using a compromise programming based multi-objective crashworthiness optimization procedure. Types of filler lattice structures (i.e., body-centered cubic, BCC and body-centered cubic with vertical strut, BCC-Z), diameter of lattice member, number of lattice unit cells and tube thickness are considered as design parameters, and the optimum values of these design parameters are sought for minimizing the peak crash force (PCF) and maximizing the specific energy absorption (SEA) values. The validated finite element models are utilized in order to construct the sample design space and carrying out results verification; an artificial neural network is employed for predicting values of the objective functions; the weighted superposition attraction algorithm is used to generate design alternatives and searching for their optimal combination. The compromise programming approach is used to combine multi-objectives and to produce various optimal design alternatives. The optimization results showed that the proposed approach is able to provide good solutions with high accuracy and proper selection of design parameters can effectively enhance the crashworthiness performance of the lattice structure filled thin-walled tubes. The optimum results revealed that BCC hybrid designs have generally superior crashworthiness performance compared to that of their BCC-Z counterparts for the same compromise solutions. In particular, the PCF value of the optimized BCC-Z hybrid structures is up to 44% higher than that of BCC hybrid structures while these structures have similar energy absorption performances. The compromise solutions also show that the SEA of BCC and BCC-Z hybrid structures increases respectively by 29% and 51% depending on the selected weight factors for the design objectives.

Application of mathematical modeling to solve problems of optimization of lattice structures

The paper deals with the application of mathematical modeling for solution of problems of optimum design of mesh structures. We will consider the method of analysis of power circuits for solving problems of structural optimization of such structures. A system for automating a computational experiment, modeling, and numerical calculation is proposed in the paper. The authors consider a mathematical model of joint deformation of the rib structure and skin, presented algorithms for solving the problem of optimal design. The problem of choosing the optimal variant of the arrangement of annular ribs in a cylindrical structure is considered as an example

On utilizing topology optimization to design support structure to prevent residual stress induced build failure in laser powder bed metal additive manufacturing

Metal additive manufacturing (AM) as an emerging manufacturing technique has been gradually accepted to manufacture end-use components. However, one of the most critical issues preventing its broad applications is build failure resulting from residual stress accumulation in manufacturing process. The goal of this work is to investigate the feasibility of using topology optimization to design support structure to mitigate residual stress induced build failure. To make topology optimization computationally tractable, the inherent strain method is employed to perform fast prediction of residual stress in an AM build. Graded lattice structure optimization is utilized to design the support structure due to the open-celled and self-supporting nature of periodic lattice structure. The objective for the optimization is to minimize the mass of sacrificial support structure under stress constraint. By limiting the maximum stress under the yield strength, cracking resulting from residual stress can be prevented. To show the feasibility of the proposed method, the support structure of a double-cantilever beam and a hip implant is designed, respectively. The support structure after optimization can achieve a weight reduction of approximately 60%. The components with optimized support structures no longer suffer from stress-induced cracking after the designs are realized by AM, which proves the effectiveness of the proposed method.

A hybrid geometric modeling method for lattice structures fabricated by additive manufacturing

Lattice structure is a type of cellular structures which is made of interconnected struts. It attracts a great research interest, since it can achieve different desired properties for a broad spectrum of applications. To generate the geometric model of lattice structures with multiscale complexities is not an easy task for most existing conventional CAD software, especially when the number of cells or struts is very large. To solve this issue, an innovative hybrid geometric modeling method is proposed in this paper. This proposed method can be divided into three steps. They are lattice frame generation, construction of geometric functions, and voxelization. A detailed description of the algorithms and data structures used in each stage are provided in this paper. Several case studies are given at the end of this paper to illustrate the effectiveness and efficiency of the proposed method. In general, by integrating the advantages of several different geometric modeling methods, the proposed method not only provides an efficient and flexible way for designers to generate different types of lattice structures for desired properties, but also offers an interface between the geometric and simulation model of lattice structures. It further removes the barrier in the design and optimization of lattice structures with multiscale complexities.

Graded-density Lattice Structure Optimization Design Based on Topology Optimization

Graded-density Lattice Structure Optimization Design Based on Topology Optimization

Finite-Element-Mesh Based Method for Modeling and Optimization of Lattice Structures for Additive Manufacturing.

A parameterization modeling method based on finite element mesh to create complex large-scale lattice structures for AM is presented, and a corresponding approach for size optimization of lattice structures is also developed. In the modeling method, meshing technique is employed to obtain the meshes and nodes of lattice structures for a given geometry. Then, a parametric description of lattice unit cells based on the element type, element nodes and their connecting relationships is developed. Once the unit cell design is selected, the initial lattice structure can be assembled by the unit cells in each finite element. Furthermore, modification of lattice structures can be operated by moving mesh nodes and changing cross-sectional areas of bars. The graded and non-uniform lattice structures can be constructed easily based on the proposed modeling method. Moreover, a size optimization algorithm based on moving iso-surface threshold (MIST) method is proposed to optimize lattice structures for enhancing the mechanical performance. To demonstrate the effectiveness of the proposed method, numerical examples and experimental testing are presented, and experimental testing shows 11% improved stiffness of the optimized non-uniform lattice structure than uniform one.

Constrained isogeometric design optimization of lattice structures on curved surfaces: computation of design velocity field

A constrained isogeometric design optimization method is presented for lattice structures located on a specified curved surface. Lattices on curved surfaces have been utilized in various engineering applications like medical stents, non-pneumatic wheel frames, and so on. When it comes to design problems, however, the lattice needs to be located on a specified surface for its manufacturability as well as performance, which results in nonlinear constraints in configuration design. We define lattice structures and their design variables on planar rectangular surfaces, and utilize the concept of free-form deformation (FFD) and the global curve interpolation to obtain the analytical expressions for the control net of lattice structure on curved surfaces. The material derivative of the analytical expressions eventually leads to precise design velocity field. The analytical configuration design sensitivity for a spatial Timoshenko beam is derived. In numerical examples, we verify the derived configuration design sensitivity and the developed computation scheme of design velocity field by comparison with finite differences, and several configuration design optimization examples are demonstrated.

Generation and optimization of lattice structure on a spur gear

This paper deals with the generation and optimization of lattice structure on a spur gear considering weight reduction of the gear as primary objective within defined displacements and stresses. A finite element model of spur gear is considered for analysis. It is optimized for a given tangential force acting on the gear tooth. Honeycomb lattice structures are generated and the structure is optimized based on the finite element analysis. Stresses and displacements of the optimized spur gear is compared with fully solid part. The obtained values of displacement for solid and optimized parts are nearly comparable. The stresses on optimized spur gear remains same as that of fully solid spur gear even after 19 % volume reduction.

Facile synthesis of highly efficient ZnO/ZnFe2O4 photocatalyst using earth-abundant sphalerite and its visible light photocatalytic activity

Micrometer-scale ZnO/ZnFe2O4 coupled photocatalyst is synthesized via a simple, one-step thermal treatment performing on natural Fe-bearing sphalerite ((Zn, Fe)S). In situ high-temperature X-ray diffraction (XRD), thermogravimetry, differential thermal analysis (TG/DTA) and scanning electron microscopy (SEM) results indicated that octahedral ZnFe2O4 (∼5 μm) formed on the surface of substrate-like ZnO (tens of microns) derived from the oxidation of sulfides upon heating to 800 °C in air for 1 h, and the two components kept stable phase ratio at 3:7 (wt%) from 900 °C (sample M-900) to 1200 °C (sample M-1200). X-ray absorption spectroscopy (XAS) and Raman spectra revealed that more Zn atoms in ZnFe2O4 of M-1200 occupied tetrahedral sites than M-900, resulting in a sharper A1g mode (∼647 cm−1), more ordered spinel structure and less antisite defects. Compared with visible-light responsive sphalerite (Zn, Fe)S, M-1200 performed more 200 nm of red-shifted optical absorption, 2.5 times at most higher the incident photon-to-electron conversion efficiency (IPCE) and 2–3-fold photocatalytic efficiency towards degradation of methyl orange and inactivation of Escherichia coli K-12. Besides, the photocatalytic activities of M-1200 preponderate over M-900, typical visible-light catalyst ZnFe2O4 and ZnO/ZnFe2O4 mechanically mixed sample. The optimization of lattice structure and the establishment of special band alignment were suggested to be remarkably beneficial to the separation of photogenerated electrons-holes and promote the photocatalytic performance. This study would enlighten a feasible and efficient strategy to fabricate coupled photocatalyst by utilizing Earth-abundant and low-cost natural minerals for solving environmental problems.

DESIGN OF STRUCTURAL PARTS BY USING MODERN SIMULATION PROCEDURES

This paper discusses modern simulation procedures used in design of structural load-carrying parts that are based on the Finite Element Method. The specific focus of the paper is the topology optimization usage within the context of two currently very interesting topics: configuration and optimization of lattice structures and modern additive manufacturing technologies. Both types of structures are presented together with their limits as well as their potentials for optimization. The discussion is illustrated by two numerical examples and experimentally obtained results. In the examples, a simple beam with three points load is optimized regarding to the different topology setups. The stress fields for different loaded optimized versions of structures are presented and the solutions are discussed and compared to the results of the experiment. A standalone topology optimization software CAESS ProTOp is used for the domain configuration and topology optimization in both examples.

Topological design optimization of lattice structures to maximize shear stiffness

To improve the poor shear performance of periodic lattice structure consisting of hexagonal unit cells, this study develops a new computational design method to apply topology optimization to search the best topological layout for lattice structures with enhanced shear stiffness. The design optimization problem of micro-cellular material is formulated based on the properties of macrostructure to maximize the shear modulus under a prescribed volume constraint using the energy-based homogenization method. The aim is to determine the optimal distribution of material phase within the periodic unit cell of lattice structure. The proposed energy-based homogenization procedure utilizes the sensitivity filter technique, especially, a modified optimal algorithm is proposed to evolve the microstructure of lattice materials with distinct topological boundaries. A high shear stiffness structure is obtained by solving the optimization model. Then, the mechanical equivalent properties are obtained and compared with those of the hexagonal honeycomb sandwich structure using a theoretical approach and the finite element method (FEM) according to the optimized structure. It demonstrates the effectiveness of the proposed method in this paper. Finally, the structure is manufactured, and then the properties are tested. Results show that the shear stiffness and bearing properties of the optimized lattice structure is better than that of the traditional honeycomb sandwich structure. In general, the proposed method can be effectively applied to the design of periodic lattice structures with high shear resistance and super bearing property.

An improved lattice structure design optimization framework considering additive manufacturing constraints

PurposeMethods to optimize lattice structure design, such as ground structure optimization, have been shown to be useful when generating efficient design concepts with complex truss-like cellular structures. Unfortunately, designs suggested by lattice structure optimization methods are often infeasible because the obtained cross-sectional parameter values cannot be fabricated by additive manufacturing (AM) processes, and it is often very difficult to transform a design proposal into one that can be additively designed. This paper aims to propose an improved, two-phase lattice structure optimization framework that considers manufacturing constraints for the AM process.Design/methodology/approachThe proposed framework uses a conventional ground structure optimization method in the first phase. In the second phase, the results from the ground structure optimization are modified according to the pre-determined manufacturing constraints using a second optimization procedure. To decrease the computational cost of the optimization process, an efficient gradient-based optimization algorithm, namely, the method of feasible directions (MFDs), is integrated into this framework. The developed framework is applied to three different design examples. The efficacy of the framework is compared to that of existing lattice structure optimization methods.FindingsThe proposed optimization framework provided designs more efficiently and with better performance than the existing optimization methods.Practical implicationsThe proposed framework can be used effectively for optimizing complex lattice-based structures.Originality/valueAn improved optimization framework that efficiently considers the AM constraints was reported for the design of lattice-based structures.

First-principles calculation of crystalline materials genome: a preliminary study

The US President Obama launched the Materials Genome Initiative on June 24, 2011, aimed at speeding up the pace of discovering, developing, manufacturing, and deploying advanced materials by at least twice as fast as is possible at present, at a fraction of the cost with the help of existing advanced computer technology. According to the authors’ understanding to the event, this article will first give a brief discussion on the origin of material genome, its scientific implication, research significance, and the far-reaching influence of materials genome study to the developments of materials science and human society. Then, the subsequent contents will introduce the research progresses of the related works carried out by the authors’ research group over the last decade, on the first-principles studies of crystalline materials genome. The highlights are focused on the method implementations for configuration optimization of lattice structure, first-principles calculations of various physical parameters on elastic, electronic, dielectric, and thermodynamic properties, and simulations of phase transition and particle transport in solids. The technical details for extending these methods to low-dimensional crystalline materials are also discussed. The article concludes with an outlook on the prospect of materials genome research.