Optimal design of lattice structures for controllable extremal band gaps

Choi, Myung-Jin; Oh, Myung‐Hwan; Koo, Bonyong; Cho, Seonho

doi:10.1038/s41598-019-46089-9

Cited by 17 publications

(14 citation statements)

References 32 publications

(35 reference statements)

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“…2: Problem definition of a spatial rod: neutral axis defined by general curve ϕ 0 (s) consistently derived from a general nonlinear formulation of [24] is utilized. The (material form) axial-shear and bending-torsional strain measures derived in [25] are evaluated at an undeformed state, which respectively result in [5] Γ(s, t) ≡ Λ 0 (s) T ∂ ∂s…”

Section: Linear Kinematics and Equilibrium Equationsmentioning

confidence: 99%

“…where (•) {j I } represents the corresponding tensor is represented in the bases of {j 1 , j 2 , j 3 }. A work done by external loads is expressed as [5] W…”

Section: Linear Kinematics and Equilibrium Equationsmentioning

confidence: 99%

“…( 11), (15), and (17) into Eq. ( 18), and applying the integration by parts lead to the following linear and angular momentum balance equations [5]…”

Section: Linear Kinematics and Equilibrium Equationsmentioning

confidence: 99%

See 2 more Smart Citations

Isogeometric configuration design optimization of three-dimensional curved beam structures for maximal fundamental frequency

Choi

Kim

Koo

et al. 2021

Struct Multidisc Optim

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This paper presents a configuration design optimization method for three-dimensional curved beam built-up structures having maximized fundamental eigenfrequency. We develop the method of computation of design velocity field and optimal design of beam structures constrained on a curved surface, where both designs of the embedded beams and the curved surface are simultaneously varied during the optimal design process. A shear-deformable beam model is used in the response analyses of structural vibrations within an isogeometric framework using the NURBS basis functions. An analytical design sensitivity expression of repeated eigenvalues is derived. The developed method is demonstrated through several illustrative examples.

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Section: Linear Kinematics and Equilibrium Equationsmentioning

confidence: 99%

“…where (•) {j I } represents the corresponding tensor is represented in the bases of {j 1 , j 2 , j 3 }. A work done by external loads is expressed as [5] W…”

Section: Linear Kinematics and Equilibrium Equationsmentioning

confidence: 99%

See 1 more Smart Citation

Isogeometric configuration design optimization of three-dimensional curved beam structures for maximal fundamental frequency

Choi

Kim

Koo

et al. 2021

Struct Multidisc Optim

Self Cite

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“…For exploring such exciting possibilities of discovering new materials with extreme properties, determining their optimal configuration at the very conceptual micro-structural design stage is indispensable 7 . A recent works with multi-material lattices 8 , pre-stressed materials 9 and piezo-embedded damped lattice metamaterials 10 , 11 show some ways of achieving extreme homogeneous properties.…”

Section: Introductionmentioning

confidence: 99%

Robust topological designs for extreme metamaterial micro-structures

Chatterjee

Chakraborty

Goswami

et al. 2021

Sci Rep

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We demonstrate that the consideration of material uncertainty can dramatically impact the optimal topological micro-structural configuration of mechanical metamaterials. The robust optimization problem is formulated in such a way that it facilitates the emergence of extreme mechanical properties of metamaterials. The algorithm is based on the bi-directional evolutionary topology optimization and energy-based homogenization approach. To simulate additive manufacturing uncertainty, combinations of spatial variation of the elastic modulus and/or, parametric variation of the Poisson’s ratio at the unit cell level are considered. Computationally parallel Monte Carlo simulations are performed to quantify the effect of input material uncertainty to the mechanical properties of interest. Results are shown for four configurations of extreme mechanical properties: (1) maximum bulk modulus (2) maximum shear modulus (3) minimum negative Poisson’s ratio (auxetic metamaterial) and (4) maximum equivalent elastic modulus. The study illustrates the importance of considering uncertainty for topology optimization of metamaterials with extreme mechanical performance. The results reveal that robust design leads to improvement in terms of (1) optimal mean performance (2) least sensitive design, and (3) elastic properties of the metamaterials compared to the corresponding deterministic design. Many interesting topological patterns have been obtained for guiding the extreme material robust design.

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“…Also, gradient based design optimizations of periodic 2D and 3D lattices is done to create and enlarge very large complete band gaps at low audible frequency ranges. 25…”

Section: Introductionmentioning

confidence: 99%

Lattice structure optimization and homogenization through finite element analyses

Vladulescu

Constantinescu

2020

Proceedings of the Institution of Mechanical Engineers, Part L:

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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.

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Optimal design of lattice structures for controllable extremal band gaps

Cited by 17 publications

References 32 publications

Isogeometric configuration design optimization of three-dimensional curved beam structures for maximal fundamental frequency

Isogeometric configuration design optimization of three-dimensional curved beam structures for maximal fundamental frequency

Robust topological designs for extreme metamaterial micro-structures

Lattice structure optimization and homogenization through finite element analyses

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