Hierarchical optimization of laminated fiber reinforced composites

Ferreira, Rafael Thiago Luiz; Rodrigues, H. C.; Guedes, J. M.; Hernandes, José Antonio

doi:10.1016/j.compstruct.2013.07.051

Cited by 46 publications

(16 citation statements)

References 28 publications

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“…To avoid the well‐known numerical instabilities in topology optimization problems, such as the checkerboards and mesh‐dependencies phenomena, some restriction must be imposed on the design. In this work, a mesh‐independent filter for discrete variables is applied to the element sensitivity numbers at both macroscale and microscale. First, the nodal sensitivity numbers

{\hat{α}}_{i}

are defined by averaging the sensitivity numbers of connected elements.…”

Section: Solution Methodsmentioning

confidence: 99%

Robust concurrent topology optimization of multiscale structure under single or multiple uncertain load cases

Cai

Wang

Zhang³

2019

Numerical Meth Engineering

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Concurrent topology optimization of macrostructure and material microstructure has attracted significant interest in recent years. However, most of the existing works assumed deterministic load conditions, thus the obtained design might have poor performance in practice when uncertainties exist. Therefore, it is necessary to take uncertainty into account in structural design. This article proposes an efficient method for robust concurrent topology optimization of multiscale structure under single or multiple load cases. The weighted sum of the mean and standard deviation of the structural compliance is minimized and constraints are imposed to both the volume fractions of macrostructure and microstructure. The effective properties of the microstructure are calculated via the homogenization method. An efficient sensitivity analysis method is proposed based on the superposition principle and orthogonal similarity transformation of real symmetric matrices. To further reduce the computational cost, an efficient decoupled sensitivity analysis method for microscale design variables is proposed. The bidirectional evolutionary structural optimization method is employed to obtain black and white designs for both macrostructure and microstructure. Several two‐dimensional and three‐dimensional numerical examples are presented to demonstrate the effectiveness of the proposed approach and the effects of load uncertainty on the optimal design of both macrostructure and microstructure.

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{\hat{α}}_{i}

are defined by averaging the sensitivity numbers of connected elements.…”

Section: Solution Methodsmentioning

confidence: 99%

Robust concurrent topology optimization of multiscale structure under single or multiple uncertain load cases

Cai

Wang

Zhang³

2019

Numerical Meth Engineering

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“…Consequently, it is not possible to account for other geometrical configurations. Such geometric variations exist in composites and their effect is explored in many studies [11,17,18]. Therefore, using the periodic RVE homogenisation approach is essential, as it can analyse general geometries [19].…”

Section: Applicationmentioning

confidence: 99%

Development of an ABAQUS plugin tool for periodic RVE homogenisation

Omairey

Dunning

Sriramula

2018

Engineering with Computers

382

131

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EasyPBC is an ABAQUS CAE plugin developed to estimate the homogenised effective elastic properties of user created periodic representative volume element (RVE), all within ABAQUS without the need to use third-party software. The plugin automatically applies the concepts of the periodic RVE homogenisation method in the software's user interface by categorising, creating, and linking sets necessary for achieving deformable periodic boundary surfaces, which can distort and no longer remain plane. Additionally, it allows the user to benefit from finite element analysis data within ABAQUS CAE interface after calculating homogenised properties. In this article, the algorithm of the plugin based on periodic RVE homogenisation method is explained, which could be developed for other commercial FE software packages. Furthermore, examples of its implementation and verification are illustrated.

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“…It is nontrivial to directly build the analytical relationship between the homogenized elasticity tensor components and the variables. Therefore, response surface modeling is applied to approximate the analytical relationship, and this method was previously applied by Ferreira et al 45 Another example about the response surface modeling of homogenized elasticity tensor is presented below. Figure 3 shows the micro-geometry of the basic material unit, in which the dark part is filled with homogeneous material of Young's modulus of 1.3 and Poisson's ratio of 0.4.…”

Section: Braidingmentioning

confidence: 99%

“…Conventionally, there are well-established theoretical basis supporting the geometry and material optimization, such as solid isotropic material penalization (SIMP), 46,47 discrete material optimization (DMO), 45,48 and evolutionary structural optimization (ESO). 49 However, in this article, the level set geometry Figure 2.…”

Section: Braidingmentioning

confidence: 99%

Computer-aided design–computer-aided engineering associative feature-based heterogeneous object modeling

Liu

Duke

2015

Advances in Mechanical Engineering

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Conventionally, heterogeneous object modeling methods paid limited attention to the concurrent modeling of geometry design and material composition distribution. Procedural method was normally employed to generate the geometry first and then determine the heterogeneous material distribution, which ignores the mutual influence. Additionally, limited capability has been established about irregular material composition distribution modeling with strong local discontinuities. This article overcomes these limitations by developing the computer-aided design-computer-aided engineering associative feature-based heterogeneous object modeling method. Level set functions are applied to model the geometry within computer-aided design module, which enables complex geometry modeling. Finite element mesh is applied to store the local material compositions within computer-aided engineering module, which allows any local discontinuities. Then, the associative feature concept builds the correspondence relationship between these modules. Additionally, the level set geometry and material optimization method are developed to concurrently generate the geometry and material information which fills the contents of the computer-aided design-computer-aided engineering associative feature model. Micro-geometry is investigated as well, instead of only the local material composition. A few cases are studied to prove the effectiveness of this new heterogeneous object modeling method. KeywordsComputer-aided design-computer-aided engineering associative feature, heterogeneous object modeling, level set, geometry and material optimization Date

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Hierarchical optimization of laminated fiber reinforced composites

Cited by 46 publications

References 28 publications

Robust concurrent topology optimization of multiscale structure under single or multiple uncertain load cases

Robust concurrent topology optimization of multiscale structure under single or multiple uncertain load cases

Development of an ABAQUS plugin tool for periodic RVE homogenisation

Computer-aided design–computer-aided engineering associative feature-based heterogeneous object modeling

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