A fuzzy optimization method for octet-truss lattices

2019 ◽  
Vol 25 (9) ◽  
pp. 1525-1535
Author(s):  
Yunhui Yang ◽  
Libin Zhao ◽  
Dexuan Qi ◽  
Meijuan Shan ◽  
Jianyu Zhang
Keyword(s):  
Mechanical Properties ◽  
Lattice Structure ◽  
Fuzzy Optimization ◽  
Material Model ◽  
Optimization Methods ◽  
Optimization Method ◽  
Optimality Criteria ◽  
Content Type ◽  
Unit Cells ◽  
Octet Truss

Purpose This paper aims to present a multiscale fuzzy optimization (FO) method to optimize both the density distribution and macrotopology of a uniform octet-truss lattice structure. Design/methodology/approach The design formulae for the strut radii are presented based on the effective mechanical properties obtained from the representative volume element. The proposed basic lattice material is applied in a normalization process to determine the material model with penalization. The solid isotropic material with penalization (SIMP) method is extended to solve the minimum compliance problem using the optimality criteria. The evolutionary deletion process is proposed to delete elements corresponding to thin-strut unit cells and to obtain the optimal macrotopology. Findings Both numerical cases indicate that the FO results significantly improved in structural performance compared with the results of the conventional SIMP. The deleting threshold controls the macrotopology of the graded-density lattice structures with negligible effects on the mechanical properties. Originality/value This paper presents one of the first multiscale optimization methods to optimize both the relative density and macrotopology of uniform octet-truss lattices. The material model and corresponding optimality criteria of octet-truss lattices are proposed and implemented in the optimization.

An improved lattice structure design optimization framework considering additive manufacturing constraints

2017 ◽  
Vol 23 (2) ◽  
pp. 305-319 ◽  
Author(s):  
Recep M. Gorguluarslan ◽  
Umesh N. Gandhi ◽  
Yuyang Song ◽  
Seung-Kyum Choi
Keyword(s):  
Additive Manufacturing ◽  
Lattice Structure ◽  
Structure Optimization ◽  
Optimization Methods ◽  
Structure Design ◽  
Second Phase ◽  
Manufacturing Constraints ◽  
Ground Structure ◽  
Content Type ◽  
Optimization Framework

Purpose Methods 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/approach The 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. Findings The proposed optimization framework provided designs more efficiently and with better performance than the existing optimization methods. Practical implications The proposed framework can be used effectively for optimizing complex lattice-based structures. Originality/value An improved optimization framework that efficiently considers the AM constraints was reported for the design of lattice-based structures.

Finite element analysis of gradient lattice structure patterns for bone implant design

2020 ◽  
Vol 11 (4) ◽  
pp. 535-545
Author(s):  
Asliah Seharing ◽  
Abdul Hadi Azman ◽  
Shahrum Abdullah
Keyword(s):  
Finite Element Analysis ◽  
Relative Density ◽  
Mechanical Behaviour ◽  
Lattice Structure ◽  
Lattice Structures ◽  
Element Analysis ◽  
Bone Implant ◽  
Content Type ◽  
Octet Truss ◽  
Structure Patterns

PurposeThe objective of this paper is to identify suitable lattice structure patterns for the design of porous bone implants manufactured using additive manufacturing.Design/methodology/approachThe study serves to compare and analyse the mechanical behaviours between cubic and octet-truss gradient lattice structures. The method used was uniaxial compression simulations using finite element analysis to identify the translational displacements.FindingsFrom the simulation results, in comparison to the cubic lattice structure, the octet-truss lattice structure showed a significant difference in mechanical behaviour. In the same design space, the translational displacement for both lattice structures increased as the relative density decreased. Apart from the relative density, the microarchitecture of the lattice structure also influenced the mechanical behaviour of the gradient lattice structure.Research limitations/implicationsGradient lattice structures are suitable for bone implant applications because of the variation of pore sizes that mimic the natural bone structures. The complex geometry that gradient lattice structures possess can be manufactured using additive manufacturing technology.Originality/valueThe results demonstrated that the cubic gradient lattice structure has the best mechanical behaviour for bone implants with appropriate relative density and pore size.

Shaping inductor geometry for casting functionally graded composites

2016 ◽  
Vol 35 (1) ◽  
pp. 16-26 ◽  
Author(s):  
Slawomir Golak ◽  
Mirosław Kordos
Keyword(s):  
Force Field ◽  
Electromagnetic Force ◽  
Low Frequency ◽  
Casting Process ◽  
Optimization Methods ◽  
Optimization Method ◽  
Functionally Graded ◽  
Matrix Composites ◽  
Content Type ◽  
Functionally Graded Composites

Purpose – The attractiveness of functionally graded composites lies in the possibility of a gradual spatial change of their properties such as hardness, strength and wear resistance. The purpose of this paper is to discuss the use of electromagnetic buoyancy to separate the reinforcement particles during the casting process of such a composite. Design/methodology/approach – The basic problem encountered in the process of casting composites is to obtain electromagnetic buoyancy and simultaneously to avoid a flow of the liquid metal which destroys the desired composite structure. In this paper the authors present the methodology of numerical optimization of inductor geometry in order to homogenize the electromagnetic force field distribution. Findings – The optimization method based on searching the solution subspace created by applying knowledge of the modelled process physics proved better than the universal local optimization methods. These results were probably caused by the complex shape of the criterion function hypersurface characterized by the presence of local minima. Practical implications – Due to their characteristics, functionally graded composites are of great interest to the automotive, aerospace and defense industries. In the case of metal matrix composites casting techniques (as the presented one) are the most effective methods of producing functionally graded materials. Originality/value – The paper presents the optimization of a new process of casting functionally graded composites in a low-frequency alternating electromagnetic field. The process involves problems that did not occur previously in the area of electromagnetic processing of materials. The paper proposes the use of special design of inductors to homogenize the electromagnetic force field.

A sequential hybrid method to establish practical sizing systems based on anthropometric data

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Amir Tjolleng ◽  
Kihyo Jung ◽  
Hyunsook Han ◽  
Hyunjung Han ◽  
Jayoung Cho
Keyword(s):  
Hybrid Method ◽  
Grid Method ◽  
Initial Step ◽  
Optimization Methods ◽  
Optimization Method ◽  
Anthropometric Data ◽  
Content Type ◽  
Subsequent Step ◽  
Sizing System ◽  
Sizing Systems

PurposeSize fit and economic efficiency are two crucial aspects that need to be considered in designing a sizing system. However, there could exist a trade-off between those aspects in order to establish a practical sizing system. The purpose of this paper is to develop a sequential hybrid method of grid and optimization to generate a practical sizing system using anthropometric data.Design/methodology/approachThe proposed sequential hybrid method consisted of two sequential steps, which employs grid method and optimization method. In the initial step, the grid method creates primary grids that accommodate a designated percentage (e.g. 90%) of users with best size fit. In the subsequent step, the optimization method generated additional grids to provide acceptable fit, with minimum fit penalty scores for users unaccommodated by the primary grids. Our method was applied to the development of a sizing system for men's military jackets. The proposed method performances were evaluated in terms of accommodation percentage, size fit and number of sizing categories.FindingsOur proposed method resulted in 26 primary grids during the initial step, which cover 90% of users. Next, we generated six additional grids during the subsequent step that provide minimum fit penalty scores for the rest (10%) users.Originality/valueThe main contributions of this paper are as follows: consider accommodation percentage, size fit and number of sizing categories in the design of sizing system; combine the grid and optimization methods and evaluate a sizing system for men's military jackets. The proposed method is applicable to develop optimal sizing systems for multiple-size products.

scholarly journals Dual Graded Lattice Structures: Generation Framework and Mechanical Properties Characterization

Polymers ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1528
Author(s):  
Khaled G. Mostafa ◽  
Guilherme A. Momesso ◽  
Xiuhui Li ◽  
David S. Nobes ◽  
Ahmed J. Qureshi
Keyword(s):  
Mechanical Properties ◽  
Relative Density ◽  
Lattice Structure ◽  
Cell Types ◽  
Functionally Graded ◽  
Unit Cell ◽  
Lattice Structures ◽  
Unit Cells ◽  
Mechanical Properties Characterization ◽  
Graded Lattice

Additive manufacturing (AM) enables the production of complex structured parts with tailored properties. Instead of manufacturing parts as fully solid, they can be infilled with lattice structures to optimize mechanical, thermal, and other functional properties. A lattice structure is formed by the repetition of a particular unit cell based on a defined pattern. The unit cell’s geometry, relative density, and size dictate the lattice structure’s properties. Where certain domains of the part require denser infill compared to other domains, the functionally graded lattice structure allows for further part optimization. This manuscript consists of two main sections. In the first section, we discussed the dual graded lattice structure (DGLS) generation framework. This framework can grade both the size and the relative density or porosity of standard and custom unit cells simultaneously as a function of the structure spatial coordinates. Popular benchmark parts from different fields were used to test the framework’s efficiency against different unit cell types and grading equations. In the second part, we investigated the effect of lattice structure dual grading on mechanical properties. It was found that combining both relative density and size grading fine-tunes the compressive strength, modulus of elasticity, absorbed energy, and fracture behavior of the lattice structure.

Impact of the Lattice Angle on the Effective Properties of the Octet-Truss Lattice Structure

2018 ◽  
Vol 140 (4) ◽  
Author(s):  
Mohamed Abdelhamid ◽  
Aleksander Czekanski
Keyword(s):  
Mechanical Properties ◽  
Relative Density ◽  
Elastic Moduli ◽  
Effective Properties ◽  
Lattice Structure ◽  
Cellular Materials ◽  
Cubic Symmetry ◽  
Shear Moduli ◽  
Octet Truss ◽  
The Impact

Cellular materials are found extensively in nature, such as wood, honeycomb, butterfly wings, and foam-like structures like trabecular bone and sponge. This class of materials proves to be structurally efficient by combining low weight with superior mechanical properties. Recent studies have shown that there are coupling relations between the mechanical properties of cellular materials and their relative density. Due to its favorable stretching‐dominated behavior, continuum models of the octet‐truss were developed to describe its effective mechanical properties. However, previous studies were only performed for the cubic symmetry case, where the lattice angle θ=45 deg. In this work, we study the impact of the lattice angle on the effective properties of the octet-truss: namely, the relative density, effective stiffness, and effective strength. The relative density formula is extended to account for different lattice angles up to a higher-order of approximation. Tensor transformations are utilized to obtain relations of the effective elastic and shear moduli, and Poisson's ratio at different lattice angles. Analytical formulas are developed to obtain the loading direction and value of the maximum and minimum specific elastic moduli at different lattice angles. In addition, tridimensional polar representations of the macroscopic strength of the octet‐truss are analyzed for different lattice angles. Finally, collapse surfaces for plastic yielding and elastic buckling are investigated for different loading combinations at different lattice angles. It has been found that lattice angles lower than 45 deg result in higher maximum values of specific effective elastic moduli, shear moduli, and strength.

scholarly journals Development of an Elastic Material Model for BCC Lattice Cell Structures Using Finite Element Analysis and Neural Networks Approaches

2019 ◽  
Vol 3 (2) ◽  
pp. 33 ◽  
Author(s):  
Tahseen Alwattar ◽  
Ahsan Mian
Keyword(s):  
Mechanical Properties ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Elastic Limit ◽  
Lattice Structure ◽  
Material Model ◽  
Element Analysis ◽  
Bcc Lattice ◽  
Lattice Cell ◽  
Cell Structures

Lattice cell structures (LCS) are being investigated for applications in sandwich composites. To obtain an optimized design, finite element analysis (FEA) -based computational approach can be used for detailed analyses of such structures, sometime at full scale. However, developing a large-scale model for a lattice-based structure is computationally expensive. If an equivalent solid FEA model can be developed using the equivalent solid mechanical properties of a lattice structure, the computational time will be greatly reduced. The main idea of this research is to develop a material model which is equivalent to the mechanical response of a lattice structure. In this study, the mechanical behavior of a body centered cubic (BCC) configuration under compression and within elastic limit is considered. First, the FEA approach and theoretical calculations are used on a single unit cell BCC for several cases (different strut diameters and cell sizes) to predict equivalent solid properties. The results are then used to develop a neural network (NN) model so that the equivalent solid properties of a BCC lattice of any configuration can be predicted. The input data of NN are bulk material properties and output data are equivalent solid mechanical properties. Two separate FEA models are then developed for samples under compression: one with 5 × 5 × 4 cell BCC and one completely solid with equivalent solid properties obtained from NN. In addition, 5 × 5 × 4 cell BCC LCS specimens are fabricated on a Fused Deposition Modeling uPrint SEplus 3D printer using Acrylonitrile Butadiene Styrene (ABS) and tested under compression. Experimental load-displacement behavior and the results obtained from both the FEA models are in good agreement within the elastic limit.

scholarly journals Compressive Behaviour of Additively Manufactured Lattice Structures: A Review

Aerospace ◽  
2021 ◽  
Vol 8 (8) ◽  
pp. 207
Author(s):  
Solomon O. Obadimu ◽  
Kyriakos I. Kourousis
Keyword(s):  
Mechanical Properties ◽  
Mechanical Performance ◽  
Lattice Structure ◽  
Evolutionary Process ◽  
Lattice Structures ◽  
Compressive Behaviour ◽  
Technology Industry ◽  
Unit Cells ◽  
Superior Mechanical Properties ◽  
And Performance

Additive manufacturing (AM) technology has undergone an evolutionary process from fabricating test products and prototypes to fabricating end-user products—a major contributing factor to this is the continuing research and development in this area. AM offers the unique opportunity to fabricate complex structures with intricate geometry such as the lattice structures. These structures are made up of struts, unit cells, and nodes, and are being used not only in the aerospace industry, but also in the sports technology industry, owing to their superior mechanical properties and performance. This paper provides a comprehensive review of the mechanical properties and performance of both metallic and non-metallic lattice structures, focusing on compressive behaviour. In particular, optimisation techniques utilised to optimise their mechanical performance are examined, as well the primary factors influencing mechanical properties of lattices, and their failure mechanisms/modes. Important AM limitations regarding lattice structure fabrication are identified from this review, while the paucity of literature regarding material extruded metal-based lattice structures is discussed.

A Generalized Optimality Criteria Method for Optimization of Additively Manufactured Multimaterial Lattice Structures

2015 ◽  
Vol 137 (11) ◽  
Author(s):  
Tino Stanković ◽  
Jochen Mueller ◽  
Paul Egan ◽  
Kristina Shea
Keyword(s):  
High Performance ◽  
Large Scale ◽  
Lattice Structure ◽  
Optimization Method ◽  
Optimality Criteria ◽  
Lattice Structures ◽  
Computational Optimization ◽  
Multiple Materials ◽  
Printed Materials ◽  
Displacement Constraints

Recent progress in additive manufacturing (AM) allows for printing customized products with multiple materials and complex geometries that could form the basis of multimaterial designs with high performance and novel functions. Effectively designing such complex products for optimal performance within the confines of AM constraints is challenging due to the need to consider fabrication constraints while searching for optimal designs with a large number of variables, which stem from new AM capabilities. In this study, fabrication constraints are addressed through empirically characterizing multiple printed materials' Young's modulus and density using a multimaterial inkjet-based 3D-printer. Data curves are modeled for the empirical data describing two base printing materials and 12 mixtures of them as inputs for a computational optimization process. An optimality criteria (OC) method is developed to search for solutions of multimaterial lattices with fixed topology and truss cross section sizes. Two representative optimization studies are presented and demonstrate higher performance with multimaterial approaches in comparison to using a single material. These include the optimization of a cubic lattice structure that must adhere to a fixed displacement constraint and a compliant beam lattice structure that must meet multiple fixed displacement constraints. Results demonstrate the feasibility of the approach as a general synthesis and optimization method for multimaterial, lightweight lattice structures that are large-scale and manufacturable on a commercial AM printer directly from the design optimization results.

A hybrid global optimization method based on multiple metamodels

2018 ◽  
Vol 35 (1) ◽  
pp. 71-90 ◽  
Author(s):  
Xiwen Cai ◽  
Haobo Qiu ◽  
Liang Gao ◽  
Xiaoke Li ◽  
Xinyu Shao
Keyword(s):  
Global Optimization ◽  
Design Optimization ◽  
Engineering Design ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Optimization Method ◽  
Expected Improvement ◽  
Benchmark Problems ◽  
Content Type ◽  
Engineering Design Optimization

Purpose This paper aims to propose hybrid global optimization based on multiple metamodels for improving the efficiency of global optimization. Design/methodology/approach The method has fully utilized the information provided by different metamodels in the optimization process. It not only imparts the expected improvement criterion of kriging into other metamodels but also intelligently selects appropriate metamodeling techniques to guide the search direction, thus making the search process very efficient. Besides, the corresponding local search strategies are also put forward to further improve the optimizing efficiency. Findings To validate the method, it is tested by several numerical benchmark problems and applied in two engineering design optimization problems. Moreover, an overall comparison between the proposed method and several other typical global optimization methods has been made. Results show that the global optimization efficiency of the proposed method is higher than that of the other methods for most situations. Originality/value The proposed method sufficiently utilizes multiple metamodels in the optimizing process. Thus, good optimizing results are obtained, showing great applicability in engineering design optimization problems which involve costly simulations.

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