Shape optimization of microstructural designs subject to local stress constraints within an XFEM-level set framework

Noël, Lise; Duysinx, Pierre

doi:10.1007/s00158-016-1642-8

Cited by 35 publications

(23 citation statements)

References 53 publications

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“…20 More recent studies have concerned multiple materials and inclusions. [21][22][23] There are also publications covering other fields of engineering, such as fluid flow, 24,25 electrostatics, 26 and magnetic actuators. 27 However, to the authors' best knowledge, there does not seem to be any previous study on level-set-based optimization using finite element methods on fixed meshes for wave propagation problems.…”

Section: Introductionmentioning

confidence: 99%

“…30 The choice of parametrization of the geometry to be optimized is crucial, since the optimization algorithm can only explore the chosen parameter space. Therefore, instead of parametrizing the design by a set of geometric primitives, 16,17,23 or an explicit boundary representation, 1 and thus bias the optimization, we choose to discretize the level-set function and use its nodal values as parameters. 11,19,20 Smoothing, or filtering, together with regularization is often applied to shape and topology optimization problems to promote smooth designs, control the feature size, counteract mesh dependence, and improve the convergence rate.…”

Section: Introductionmentioning

confidence: 99%

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Acoustic shape optimization using cut finite elements

Bernland

Wadbro

Berggren

2017

Numerical Meth Engineering

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Fictitious domain methods are attractive for shape optimization applications, since they do not require deformed or regenerated meshes. A recently developed such method is the CutFEM approach, which allows crisp boundary representations and for which uniformly well-conditioned system matrices can be guaranteed. Here, we investigate the use of the CutFEM approach for acoustic shape optimization, using as test problem the design of an acoustic horn for favorable impedance-matching properties. The CutFEM approach is used to solve the Helmholtz equation, and the geometry of the horn is implicitly described by a level-set function. To promote smooth algorithmic updates of the geometry, we propose to use the nodal values of the Laplacian of the level-set function as design variables. This strategy also improves the algorithm's convergence rate, counteracts mesh dependence, and, in combination with Tikhonov regularization, controls small details in the optimized designs. An advantage with the proposed method is that the exact derivatives of the discrete objective function can be expressed as boundary integrals, as opposed to when using a traditional method that uses mesh deformations. The resulting horns possess excellent impedance-matching properties and exhibit surprising subwavelength structures, not previously seen, which are possible to capture due to the fixed mesh approach.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Acoustic shape optimization using cut finite elements

Bernland

Wadbro

Berggren

2017

Numerical Meth Engineering

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“…This approach is particularly suited to optimization as it uses a mesh that does not conform to the shape of the microstructure, thereby bypassing mesh distortion issues associated with other shape optimization methods. Other optimization studies of PUCs are available in the literature [25][26][27][28] but these studies are based on weakly discontinuous (C 0 ) interface enrichment functions used to model perfect (nonfailing) interfaces.…”

Section: Introductionmentioning

confidence: 99%

Multiscale design of three‐dimensional nonlinear composites using an interface‐enriched generalized finite element method

Brandyberry

Najafi

Geubelle

2020

Numerical Meth Engineering

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A computational framework is developed to model and optimize the nonlinear multiscale response of three-dimensional particulate composites using an interface-enriched generalized finite element method. The material nonlinearities are associated with interfacial debonding of inclusions from a surrounding matrix which is modeled using C −1 continuous enrichment functions and a cohesive failure model. Analytic material and shape sensitivities of the homogenized constitutive response are derived and used to drive a nonlinear inverse homogenization problem using gradient-based optimization methods. Spherical and ellipsoidal particulate microstructures are designed to match a component of the homogenized stress-strain response to a desired constructed macroscopic stress-strain behavior. K E Y W O R D Sanalytic sensitivity, cohesive failure, composites, multiscale modeling, shape optimization 1 2806

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“…This can be rather a simple task for structural optimization techniques [1]. Structural optimization methods can be broadly divided into three categories, namely, size optimization [2], shape optimization [3,4], and topology optimization [5][6][7][8][9][10][11] methods.…”

Section: Introductionmentioning

confidence: 99%

A Novel Design Framework for Structures/Materials with Enhanced Mechanical Performances

Liu¹,

Fan²,

Wen³

et al. 2018

Preprint

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Structure/material requires simultaneous consideration of both its design and manufacturing processes to dramatically enhance its manufacturability, assembly and maintainability. In this work, we present a novel design framework for structure/material with requested mechanical performances in virtue of the compelling properties of topological design and origami techniques. The framework comprises four procedures, including topological design, unfold, reduction manufacturing, and fold. Topological design method, i.e. Solid Isotropic Material Penalization (SIMP) method, serves to optimize the structure to achieve preferred mechanical characteristics and origami technique is exploited to make the structure rapidly and easily fabricated. Topological design and unfold procedures can be conveniently completed in a computer; then, reduction manufacturing, i.e. cutting, is performed to remove materials from the unfolded flat plate; the final structure is finally obtained by folding the plate of the previous procedure. A series of cantilevers, consisting of origami with parallel creases and Miura-ori (usually regarded as a metamaterial), made of paperboard are designed with least weight and required stiffness by using the proposed framework. The findings here furnish an alternative design framework for engineering structures which could be better than 3D printing technique, especially for large structures made of thin metal materials.

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Shape optimization of microstructural designs subject to local stress constraints within an XFEM-level set framework

Cited by 35 publications

References 53 publications

Acoustic shape optimization using cut finite elements

Acoustic shape optimization using cut finite elements

Multiscale design of three‐dimensional nonlinear composites using an interface‐enriched generalized finite element method

A Novel Design Framework for Structures/Materials with Enhanced Mechanical Performances

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