Inverse homogenization using isogeometric shape optimization

Lüdeker, Julian Kajo; Sigmund, Ole; Kriegesmann, Benedikt

doi:10.1016/j.cma.2020.113170

Cited by 13 publications

(4 citation statements)

References 41 publications

(57 reference statements)

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“…The IGA-based shape optimization for periodic material microstructures using the inverse homogenization was also studied in Ref. [114]. The introducing of IGA into topology optimization for the rational design of auxetic metamaterials can track to Ref.…”

Section: Mechanical Metamaterialsmentioning

confidence: 99%

A Comprehensive Review of Isogeometric Topology Optimization: Methods, Applications and Prospects

Gao

Xiao

Zhang

et al. 2020

Chin. J. Mech. Eng.

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Topology Optimization (TO) is a powerful numerical technique to determine the optimal material layout in a design domain, which has accepted considerable developments in recent years. The classic Finite Element Method (FEM) is applied to compute the unknown structural responses in TO. However, several numerical deficiencies of the FEM significantly influence the effectiveness and efficiency of TO. In order to eliminate the negative influence of the FEM on TO, IsoGeometric Analysis (IGA) has become a promising alternative due to its unique feature that the Computer-Aided Design (CAD) model and Computer-Aided Engineering (CAE) model can be unified into a same mathematical model. In the paper, the main intention is to provide a comprehensive overview for the developments of Isogeometric Topology Optimization (ITO) in methods and applications. Finally, some prospects for the developments of ITO in the future are also presented.

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Section: Mechanical Metamaterialsmentioning

confidence: 99%

A Comprehensive Review of Isogeometric Topology Optimization: Methods, Applications and Prospects

Gao

Xiao

Zhang

et al. 2020

Chin. J. Mech. Eng.

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“…It can be shown [44] that optimal closed-walled microstructures are always stiffer up to a factor of 3 compared to their open truss lattice counterparts for arbitrary loadings. Realizing multiscale rank-n structures is challenging, but single scale realizations of these may approach the bounds with less than 10% error [45,46,33,47].…”

Section: Extended Summary With Referencesmentioning

confidence: 99%

EML webinar overview: Topology Optimization — Status and Perspectives

Sigmund

2020

Extreme Mechanics Letters

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“…When traditional BEM meshes are used for geometric parameterization, it leads to jaggedness in the optimized geometry, as is already known in the finite element method [14]. To address this challenge, geometries in shape optimization are often parameterized using B-splines or related techniques, such as NURBS [15,16] and subdivision surfaces [17][18][19][20]. In this research, we represent the domain geometries in terms of subdivision surfaces, which are spline extensions of arbitrarily connected meshes.…”

Section: Introductionmentioning

confidence: 99%

A Subdivision-Based Combined Shape and Topology Optimization in Acoustics

Lu,

Chen,

Luo

et al. 2024

CMES

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We propose a combined shape and topology optimization approach in this research for 3D acoustics by using the isogeometric boundary element method with subdivision surfaces. The existing structural optimization methods mainly contain shape and topology schemes, with the former changing the surface geometric profile of the structure and the latter changing the material distribution topology or hole topology of the structure. In the present acoustic performance optimization, the coordinates of the control points in the subdivision surfaces fine mesh are selected as the shape design parameters of the structure, the artificial density of the sound absorbing material covered on the structure surface is set as the topology design parameter, and the combined topology and shape optimization approach is established through the sound field analysis of the subdivision surfaces boundary element method as a bridge. The topology and shape sensitivities of the approach are calculated using the adjoint variable method, which ensures the efficiency of the optimization. The geometric jaggedness and material distribution discontinuities that appear in the optimization process are overcome to a certain degree by the multiresolution method and solid isotropic material with penalization. Numerical examples are given to validate the effectiveness of the presented optimization approach.

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Inverse homogenization using isogeometric shape optimization

Cited by 13 publications

References 41 publications

A Comprehensive Review of Isogeometric Topology Optimization: Methods, Applications and Prospects

A Comprehensive Review of Isogeometric Topology Optimization: Methods, Applications and Prospects

EML webinar overview: Topology Optimization — Status and Perspectives

A Subdivision-Based Combined Shape and Topology Optimization in Acoustics

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