Towards the stabilization of the low density elements in topology optimization with large deformation

Lahuerta, Ricardo Doll; Simões, Eduardo T.; Campello, Eduardo M. B.; Pimenta, Paulo de Mattos; Silva, Emilio C.

doi:10.1007/s00466-013-0843-x

Cited by 64 publications

(44 citation statements)

References 38 publications

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“…Yoon and Kim [9] proposed a method that uses connectivity between elements as the design variables of topology optimization. In addition, Lahuerta et al [10] and Wang et al [11] proposed to tailor the material model of the artificial weak material such that the numerical instability can be eliminated. Meshless methods were also proposed by Cho and Kwak [12] and He et al [13] to overcome the numerical instability.…”

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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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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“…To overcome this issue, Bruns and Tortorelli (2003) proposed totally removing low-density elements. To stabilize the excessive distortion of low-density elements, Lahuerta et al (2013) proposed the use of a polyconvex constitutive model in conjunction with a relaxation function. proposed a new interpolation scheme in which the strain energy density (SED) of low-density elements and high-density elements was modelled using small deformation theory and large deformation theory, respectively.…”

Section: Introductionmentioning

confidence: 99%

Topology optimization of geometrically nonlinear structures using an evolutionary optimization method

Abdi

Ashcroft

Wildman

2018

Engineering Optimization

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A note on versions:The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription. ABSTRACTThe topology optimization using isolines/isosurfaces and extended finite element method (Iso-XFEM) is an evolutionary optimization method developed in previous studies to enable the generation of high-resolution topology optimized designs suitable for additive manufacture. Conventional approaches for topology optimization require additional postprocessing after optimization to generate a manufacturable topology with clearly defined smooth boundaries. Iso-XFEM aims to eliminate this timeconsuming post-processing stage by defining the boundaries using isovalues of a structural performance criterion and an extended finite element method (XFEM) scheme. In this article, the Iso-XFEM method is further developed to enable the topology optimization of geometrically nonlinear structures undergoing large deformations. This is achieved by implementing a total Lagrangian finite element formulation and defining a structural performance criterion appropriate for the objective function of the optimization problem. The Iso-XFEM solutions for geometrically nonlinear test cases implementing linear and nonlinear modelling are compared, and the suitability of nonlinear modelling for the topology optimization of geometrically nonlinear structures is investigated. ARTICLE HISTORY

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“…O modelo de materialé aplicado na forma fraca do variacional do sistema multiplicando neste caso a função de energia de deformação específica de uma lei material (Lahuerta et al, 2013) (Bendsøe, 1989), a função referente ao modelo material SIMPé dada por:…”

Section: Modelo De Materials -Simpunclassified

“…Na equação (4.5)é apresentado de forma clara ondeé aplicado o modelo de material no MOT como apresentado a seguir nas matrizes de elemento finito (Bendsøe, 1989;Lahuerta et al, 2013) permite mitigar a formação da escala de cinza na topologia …”

Section: Modelo De Materials -Simpunclassified

“…Isto significa que os parâmetros de penalização inicial e a ocorrência do seu incremento pode alterar a topologia final da estrutura. Tais resultados são apresentados por Lahuerta et al (2013), ondeé possível observar a ocorrência deste efeito. A ideia de utilizar uma função de continuação do parâmetro de penalizaçãoé evitar esta dependência no SIMP, alterando de forma gradualmente a seu valor, tornando desta forma o problema menos dependente dos valores iniciais de penalização no modelo material.…”

Section: Função De Continuaçãounclassified

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Projeto de mecanismos flexíveis baseado no efeito da flambagem não linear utilizando o método de otimização topológica.

Lahuerta¹

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Towards the stabilization of the low density elements in topology optimization with large deformation

Cited by 64 publications

References 38 publications

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

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

Topology optimization of geometrically nonlinear structures using an evolutionary optimization method

Projeto de mecanismos flexíveis baseado no efeito da flambagem não linear utilizando o método de otimização topológica.

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