Level set based topological shape optimization of geometrically nonlinear structures using unstructured mesh

Ha, Seung‐Hyun; Cho, Seonho

doi:10.1016/j.compstruc.2007.05.025

Cited by 67 publications

(46 citation statements)

References 19 publications

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“…Furthermore, a maximum von Mises stress constraint has been enforced in topology optimization problems (e.g. Duysinx and Sigmund (1998); Svanberg and Werme (2007); Bruggi and Venini (2008); Le et al (2010); Cheng and Jiang (1992); Allaire and Jouve (2008); Allaire et al (2011Allaire et al ( , 2014; Ha and Cho (2008); Yamasaki et al (2011)) and a number of other papers. In the work of (Amstutz and Novotny 2010) the authors present a topology optimization method which utilizes a p-norm stress measure with very high p's such that the locality of stresses is resolved.…”

Section: Introductionmentioning

confidence: 99%

Combined shape and topology optimization for minimization of maximal von Mises stress

Lian

Christiansen

Tortorelli

et al. 2017

Struct Multidisc Optim

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Section: Introductionmentioning

confidence: 99%

Combined shape and topology optimization for minimization of maximal von Mises stress

Lian

Christiansen

Tortorelli

et al. 2017

Struct Multidisc Optim

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“…In the present work, being similar to the method proposed by Ha and Cho [14], we do the finite element analysis by modifying a fixed background mesh and do not use the artificial weak material, as proposed in our previous study [15] and used in [25,33]. A similar method was also proposed by Allaire et al [34].…”

Section: Finite Element Analysismentioning

confidence: 99%

“…Meshless methods were also proposed by Cho and Kwak [12] and He et al [13] to overcome the numerical instability. In a level set based solution to the topology optimization of geometrically nonlinear structures, remesh is proposed by Ha and Cho [14] to obtain a mesh that is conformal to the geometry of the structure, thus eliminating the artificial weak material as well as the numerical instability coming with it. In the present study, being similar to the method proposed by Ha and Cho [14], we do the finite element analysis by modifying a fixed background mesh and do not use the artificial weak material, as proposed in our previous study [15].…”

Section: Introductionmentioning

confidence: 99%

Stiffness optimization of geometrically nonlinear structures and the level set based solution

Xia

Shi

2016

Int. J. Simul. Multisci. Des. Optim.

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-Load-normalized strain energy increments between consecutive load steps are aggregated through the Kreisselmeier-Steinhauser (KS) function, and the KS function is proposed as a stiffness criterion of geometrically nonlinear structures. A topology optimization problem is defined to minimize the KS function together with the perimeter of structure and a volume constraint. The finite element analysis is done by remeshing, and artificial weak material is not used. The topology optimization problem is solved by using the level set method. Several numerical examples in two dimensions are provided. Other criteria of stiffness, i.e., the end compliance and the complementary work, are compared.

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“…설계민감도 해석기법은 선형 및 비선형 문제, 열, 유체, 지능재료 등 다양한 문제에 대하여 개발되어 왔다 (Ha et al, 2008;2006). 설계민감도는 설계변수에 대한 성능함수 의 변분값이다 (Haug et al, 1986).…”

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Shape Design Optimization of Crack Propagation ProblemsUsing Meshfree Methods

Kim¹,

Ha²,

Cho³

2014

jcoseik

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This paper presents a continuum-based shape design sensitivity analysis(DSA) method for crack propagation problems using a reproducing kernel method(RKM), which facilitates the remeshing problem required for finite element analysis(FEA) and provides the higher order shape functions by increasing the continuity of the kernel functions. A linear elasticity is considered to obtain the required stress field around the crack tip for the evaluation of J-integral. The sensitivity of displacement field and stress intensity factor(SIF) with respect to shape design variables are derived using a material derivative approach. For efficient computation of design sensitivity, an adjoint variable method is employed tather than the direct differentiation method. Through numerical examples, The mesh-free and the DSA methods show excellent agreement with finite difference results. The DSA results are further extended to a shape optimization of crack propagation problems to control the propagation path.

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Level set based topological shape optimization of geometrically nonlinear structures using unstructured mesh

Cited by 67 publications

References 19 publications

Combined shape and topology optimization for minimization of maximal von Mises stress

Combined shape and topology optimization for minimization of maximal von Mises stress

Stiffness optimization of geometrically nonlinear structures and the level set based solution

Shape Design Optimization of Crack Propagation ProblemsUsing Meshfree Methods

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