Topology optimization for concurrent design of layer-wise graded lattice materials and structures

Zhang, Hui-Kai; Wang, Yaguang; Kang, Zhan

doi:10.1016/j.ijengsci.2019.01.006

Cited by 64 publications

(17 citation statements)

References 54 publications

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“…This concurrent method is termed here as Multiscale Topology Optimization with Cellular Materials (MTOCM), and it is graphically explained in Figure 10. Examples of relevant works using MTOCM approach can be found in [171][172][173][174][175]. The second concurrent methodology consists in modifying the relative density of the cellular design domain based on a Topology Optimization process, obtaining the socalled functionally graded Cellular Materials.…”

Section: Tailoring Stiffness Via Topology Optimizationmentioning

confidence: 99%

A Review on Tailoring Stiffness in Compliant Systems, via Removing Material: Cellular Materials and Topology Optimization

2021

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Cellular Materials and Topology Optimization use a structured distribution of material to achieve specific mechanical properties. The controlled distribution of material often leads to several advantages including the customization of the resulting mechanical properties; this can be achieved following these two approaches. In this work, a review of these two as approaches used with compliance purposes applied at flexure level is presented. The related literature is assessed with the aim of clarifying how they can be used in tailoring stiffness of flexure elements. Basic concepts needed to understand the fundamental process of each approach are presented. Further, tailoring stiffness is described as an evolutionary process used in compliance applications. Additionally, works that used these approaches to tailor stiffness of flexure elements are described and categorized. Finally, concluding remarks and recommendations to further extend the study of these two approaches in tailoring the stiffness of flexure elements are discussed.

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Section: Tailoring Stiffness Via Topology Optimizationmentioning

confidence: 99%

A Review on Tailoring Stiffness in Compliant Systems, via Removing Material: Cellular Materials and Topology Optimization

2021

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“…It is common practice to model lattice microstructures as continuous solid medium, wherein a unit cell based approach can be adopted to obtain the effective elastic moduli for the entire solid domain [15,52,53,54,55]. It has been shown theoretically that lattice materials with hexagonal honeycomb-like structures can exhibit negative Young's modulus under a dynamic environment [50].…”

Section: Theoretical Background For Negative Young's Modulimentioning

confidence: 99%

Apparent negative values of Young’s moduli of lattice materials under dynamic conditions

Adhikari

Mukhopadhyay

Shaw

et al. 2020

International Journal of Engineering Science

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Lattice materials are characterised by their equivalent elastic moduli for analysing mechanical properties of the microstructures. The values of the elastic moduli under static forcing condition are primarily dependent on the geometric properties of the constituent unit cell and the mechanical properties of the intrinsic material. Under a static forcing condition, the equivalent elastic moduli (such as Young's modulus) are always positive. When dynamic forcing is considered, the equivalent elastic moduli become functions of the applied frequency and they can be negative at certain frequency values. This paper, for the first time, explicitly demonstrates the occurrence of negative equivalent Young's modulus in lattice materials experimentally. Using additively manufactured titanium-alloy lattice metastructures, it is shown that the real part of experimentally measured in-plane Young's modulus becomes negative under a dynamic environment. In fact, we show that the onset of such negative Young's modulus in lattice materials can be precisely determined by capturing the subwavelength scale dynamics of the system. Experimental confirmation of the negative Young's moduli and the onset of the same as a function of frequency provide the necessary physical insights and confidence for its potential exploitation in various multi-functional structural systems and devices across different length scales.

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“…In [74], a neural network is trained to compute a homogenized elasticity tensor as a function of selected geometric parameters of a unit cell and the microscale parameters are incorporated in a macroscale density-based optimization. In [78], homogenization is used to design layer-wise graded lattice materials. Some hybrid methods that combine the concepts of the homogenization of unit cell design and the control of the cross-sectional areas of bars are developed in [22].There are too many other works using homogenization to compute effective material properties to describe here; some of the research most pertinent to design of lattice-type structures includes: [73,72,29].…”

Section: Introductionmentioning

confidence: 99%

Component-wise reduced order model lattice-type structure design

McBane,

Choi

2020

Preprint

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Lattice-type structures can provide a combination of stiffness with light weight that is desirable in a variety of applications. Design optimization of these structures must rely on approximations of the governing physics to render solution of a mathematical model feasible. In this paper, we propose a topology optimization (TO) formulation that approximates the governing physics using component-wise reduced order modeling as introduced in [46] and [33], which can reduce solution time by multiple orders of magnitude over a full-order finite element model while providing a relative error in the solution of <1%. In addition, the offline training data set from such component-wise models is reusable, allowing its application to many design problems for only the cost of a single offline training phase, and the component-wise method is nearly embarrassingly parallel. We also show how the parameterization chosen in our optimization allows a simplification of the component-wise reduced order model (CWROM) not noted in previous literature, for further speedup of the optimization process. The sensitivity of the compliance with respect to the particular parameterization is derived solely in the component level. In numerical examples, we demonstrate a 1000x speedup over a full-order FEM model with relative error of <1% and show minimum compliance designs for two different cantilever beam examples, one smaller and one larger. Finally, error bounds for displacement field, compliance, and compliance sensitivity of the CWROM are derived.

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Topology optimization for concurrent design of layer-wise graded lattice materials and structures

Cited by 64 publications

References 54 publications

A Review on Tailoring Stiffness in Compliant Systems, via Removing Material: Cellular Materials and Topology Optimization

A Review on Tailoring Stiffness in Compliant Systems, via Removing Material: Cellular Materials and Topology Optimization

Apparent negative values of Young’s moduli of lattice materials under dynamic conditions

Component-wise reduced order model lattice-type structure design

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