An integrated homogenization–based topology optimization via RBF mapping strategies for additively manufactured FGLS and its application to bandgap structures

Şimşek, Uğur; Gayir, Cemal Efe; Kızıltaş, Güllü; Şendur, Polat

doi:10.1007/s00170-020-06207-8

Cited by 13 publications

(10 citation statements)

References 27 publications

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“…Fueled by the recent developments in advanced optimization techniques, including machine learning, recent years have witnessed a growing interest in implementing these techniques to further push the boundaries of density-graded structures. These optimization tools (e.g., topology optimization, [203][204][205] genetic algorithms, [206] and machine learning [207,208] ) have been used at the microscopic-(i.e., the architecture of the cells) and the macroscopic-level [209][210][211] (i.e., the mesoscale geometry and gradation of the cellular structures) designs in the search for lattice and cellular geometries that lead to optimal mechanical properties at reduced structural weights. For example, using a gradientbased algorithm, Wang et al [212] determined the optimal truss lattice structure for arbitrary loadings in the low-volume limit.…”

Section: Current and Future Efforts In Property Optimization Of Grade...mentioning

confidence: 99%

Density‐Graded Cellular Solids: Mechanics, Fabrication, and Applications

et al. 2021

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Cellular solids have gained extensive popularity in different areas of engineering due to their unique physical and mechanical properties. Recent advancements in manufacturing technologies have led to the development of cellular solids with highly controllable microstructures and properties modulated for multiple functionalities at low structural weights. The concept of density gradation in cellular solids has recently gained attention due to its potentials in opening new doors to the development of lightweight structures that offer optimal physical and mechanical properties without compromising their favorable characteristics. Herein, a comprehensive insight into the fundamental concepts, fabrication, and current and potential applications of density‐graded cellular solids in various areas of science and engineering is provided. Cellular solids are broadly classified into two main categories: foams and lattice structures. An overview of the fundamental concepts in each category is presented, followed by details on the characterization approaches and some of the most novel processing techniques utilized in fabricating the structures. The uses of density‐graded structures in load‐bearing, acoustic, and biomedical applications are highlighted. The state of the art in each category and the current trends in application‐specific optimization of density‐graded structures are discussed. The review concludes with an outlook of the future directions in this exciting field.

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Section: Current and Future Efforts In Property Optimization Of Grade...mentioning

confidence: 99%

Density‐Graded Cellular Solids: Mechanics, Fabrication, and Applications

et al. 2021

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“…The SIMP algorithm, which relates the relative density of a finite element to elastic modulus using Equation (), is one of the most used mathematical forms of the TO approaches

E_{normale} = E_{normals} (ρ_{normale})^{p}

where E e and ρ e are the elastic modulus and the relative density of the e th finite element, respectively, and p ( p ≥ 1) is the penalization factor. Simsek et al [ 24 ] proposed a modified SIMP method based on the Gibson–Ashby model to represent lattice properties and consider the intermediate element densities in the HMTO algorithm as shown in Equation ()

E_{normale} / E_{normals} = C_{1}^{*} (ρ_{normale})^{p^{*}}

where

C_{1}^{*}

and p * are the constants of the Gibson–Ashby. Different penalization factors on the relative elastic modulus are shown for D‐, G‐, and I‐WP‐type lattices in Figure .…”

Section: Optimization Approachesmentioning

confidence: 99%

“…where E e and ρ e are the elastic modulus and the relative density of the eth finite element, respectively, and p(p ≥ 1) is the penalization factor. Simsek et al [24] proposed a modified SIMP method based on the Gibson-Ashby model to represent lattice properties and consider the intermediate element densities in the HMTO algorithm as shown in Equation ( 12)…”

Section: Modified Simpmentioning

confidence: 99%

“…[ 22 ] Groen and Sigmund used this method to produce manufacturable designs with high resolution. [ 23 ] In a more recent study, Simsek et al [ 24 ] proposed the application of the HMTO optimization with a modified SIMP method to double gyroid (DG) surface‐based lattice structures. The application of this algorithm for other types of lattice structures was acknowledged as future work in that study.…”

Section: Introductionmentioning

confidence: 99%

“…This article is an extension of authors' previous studies. [24,25,34] In this study, the design for additive manufacturing (DfAM) technique is used to determine the best material distribution in a design domain using HMTO and FOGLG methodologies for different lattice types. More specifically, HMTO and FOGLG methods are demonstrated and compared for D, G, and I-WP in this study.…”

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confidence: 99%

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Experimental and Numerical Modal Characterization for Additively Manufactured Triply Periodic Minimal Surface Lattice Structures: Comparison between Free‐Size and Homogenization‐Based Optimization Methods

Ozdemir

Şimşek²,

Kuser

et al. 2023

Adv Eng Mater

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Additive manufacturing (AM), a substantial breakthrough over traditional manufacturing processes, has evolved significantly over the last few decades to meet industry demand. [1,2] It enables designers to utilize nature-inspired complex structures such as triply periodic minimal surface (TPMS) lattice structures. [3][4][5] The TPMS structures are desired and topologically ordered in many design applications due to their attractive properties, such as being lightweight and enhanced mechanical properties. [6,7] Another advantage of these structures is that their mechanical performance and functionality can be further improved by altering the thickness of given structures. [8][9][10] The quest for the ideal structure prompts new optimization proposals in the literature. Topology optimization (TO), which defines the best material distribution within the design domain, is one of the most extensively utilized optimization methods in the literature. [11][12][13] Among the various mathematical methods for TO, the solid isotropic material with penalization (SIMP), proposed by Rozvany et al., [14] gained significant attention due to its simplicity in implementation for the TO. The application of this approach to generate multiclass microstructures made of truss elements is available in the literature. For example, surrogate models for different truss-based structures are used in TO to minimize the compliance of the structure for a given volume ratio. The methodology was demonstrated on 2D and 3D case studies. [15] In another study, [16]

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A new sensitivity-based mapping scheme for topology optimization of graded TPMS designs

Parlayan,

Ozdemir,

Gayir

et al. 2023

Int J Adv Manuf Technol

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Graded TPMS topologies display excellent mechanical and thermal properties. Design schemes targeting optimal performance exist, but final reconstructed designs still suffer from performance degradation. To overcome this challenge, we propose an automated design framework based on the integration of a homogenization-based topology optimization scheme and a new mapping strategy. Optimized designs obtained using a modified SIMP technique are reconstructed as graded gyroid structures. Unlike mapping strategies using relative density values prior to TPMS infill, for the first time we make use of readily available adjoint sensitivities for mapping optimal densities to graded gyroid structures. Results show that the proposed framework delivers performance preserving graded designs when compared to original optimized designs obtained using OPTISTRUCT and superior performance in comparison to standard density-based mapping methods. The resulting graded design is manufactured using additive manufacturing and three-point bending tests are performed confirming simulation results and demonstrating the applicability of presented design scheme.

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An integrated homogenization–based topology optimization via RBF mapping strategies for additively manufactured FGLS and its application to bandgap structures

Cited by 13 publications

References 27 publications

Density‐Graded Cellular Solids: Mechanics, Fabrication, and Applications

Density‐Graded Cellular Solids: Mechanics, Fabrication, and Applications

Experimental and Numerical Modal Characterization for Additively Manufactured Triply Periodic Minimal Surface Lattice Structures: Comparison between Free‐Size and Homogenization‐Based Optimization Methods

A new sensitivity-based mapping scheme for topology optimization of graded TPMS designs

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