Robust topology optimization for multiple fiber-reinforced plastic (FRP) composites under loading uncertainties

Xu, Yanan; Gao, Yunkai; Wu, Chi; Fang, Jianguang; Li, Qing

doi:10.1007/s00158-018-2175-0

Cited by 48 publications

(13 citation statements)

References 43 publications

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“…The mathematical expression of the material model can be given as, 13,43

{boldE}_{italicjl} false(x_{jlc} false) = {boldE}_{0} + \sum_{c = 1}^{n^{c}} \frac{x_{jlc}}{1 + q false(1 - x_{italicjlc} false)} false({boldE}_{c} - {boldE}_{0} false)

where

{boldE}_{italicjl}

denotes the constitutive material matrix for layer

l

in domain

j

{boldE}_{0}

means the constitutive matrix of an artificial material to avoid singularity due to presence of void material properties, and

{boldE}_{c}

represents the constitutive matrix of candidate orientation

c

q

is the penalization parameter for RAMP which pushes the design variables

x_{italicjlc}

towards their discrete optimum.…”

Section: Methodsmentioning

confidence: 99%

“…More derivation details of sensitivities can be found in References 37,43. Many mathematical programming algorithms exhibit excellent performance in structural design and topology optimization.…”

Section: Methodsmentioning

confidence: 99%

“…In this benchmark design example as well as the engine hood design example in Section 5, the same material properties of unidirectional (UD) carbon fiber reinforced plastic (CFRP) composites are used as in Table 2. 43 In the both problems, the mean compliance is considered to be the design objective. The design problem can be mathematically formulated as,…”

Section: Benchmark Design Examplementioning

confidence: 99%

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Machine learning based topology optimization of fiber orientation for variable stiffness composite structures

Gao

et al. 2021

Numerical Meth Engineering

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This study proposes a machine learning (ML) based approach for optimizing fiber orientations of variable stiffness carbon fiber reinforced plastic (CFRP) structures, where neural networks are developed to estimate the objective function and analytical sensitivities with respect to design variables as a substitute for finite element analysis (FEA). To reduce the number of training samples and improve the regression accuracy, an active learning strategy is implemented by successively supplying effective samples along with the suboptimal process.After proper training of neural networks, a quasi-global search strategy can be applied by implementing a large number of initial designs as starting points in the optimization. In this article, a mathematical example is first presented to show the superiority of the active learning strategy. Then a benchmark design example of a CFRP plate is scrutinized to compare the proposed ML-based with the conventional FEA-based discrete material optimization (DMO) method.Finally, topology optimization of fiber orientations is performed for design of a CFRP engine hood, in which the structural performance generated from the proposed ML-based approach achieves 12.62% improvement compared with that obtained from the conventional single-initial design method. This article is anticipated to demonstrate a new alternative for design of fiber-reinforced composite structures.

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“…The mathematical expression of the material model can be given as, 13,43

{boldE}_{italicjl} false(x_{jlc} false) = {boldE}_{0} + \sum_{c = 1}^{n^{c}} \frac{x_{jlc}}{1 + q false(1 - x_{italicjlc} false)} false({boldE}_{c} - {boldE}_{0} false)

where

{boldE}_{italicjl}

denotes the constitutive material matrix for layer

l

in domain

j

{boldE}_{0}

means the constitutive matrix of an artificial material to avoid singularity due to presence of void material properties, and

{boldE}_{c}

represents the constitutive matrix of candidate orientation

c

q

is the penalization parameter for RAMP which pushes the design variables

x_{italicjlc}

towards their discrete optimum.…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Benchmark Design Examplementioning

confidence: 99%

See 1 more Smart Citation

Machine learning based topology optimization of fiber orientation for variable stiffness composite structures

Gao

et al. 2021

Numerical Meth Engineering

Self Cite

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show abstract

“…An improved curvilinear parameterization method [51,54] exploits the Level Set method to optimize fiber paths by enforcing the continuity of fiber angles at the element interfaces [10]. In [56] the authors proposed a nondeterministic robust topology optimization of ply orientation for multiple fiber-reinforced plastic materials under loading uncertainties.…”

Section: Introductionmentioning

confidence: 99%

Stacking sequences in composite laminates through design optimization

et al. 2020

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Composites are experiencing a new era. The spatial resolution at which is to date possible to build up complex architectured microstructures through additive manufacturing-based and sintering of powder metals 3D printing techniques, as well as the recent improvements in both filament winding and automated fiber deposition processes, are opening new unforeseeable scenarios for applying optimization strategies to the design of high-performance structures and metamaterials that could previously be only theoretically conceived. Motivated by these new possibilities, the present work, by combining computational methods, analytical approaches and experimental analysis, shows how finite element Design Optimization algorithms can be ad hoc rewritten by identifying as design variables the orientation of the reinforcing fibers in each ply of a layered structure for redesigning fiber-reinforced composites exhibiting at the same time high stiffness and toughening, two features generally in competition each other. To highlight the flexibility and the effectiveness of the proposed strategy, after a brief recalling of the essential theoretical remarks and the implemented procedure, selected example applications are finally illustrated on laminated plates under different boundary conditions, cylindrical layered shells with varying curvature subjected to point loads and composite tubes made of carbon fiber-reinforced polymers, recently employed as structural components in advanced aerospace engineering applications.

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“…Although concurrent topology optimization of macrostructure and material microstructure has made great progress, most of the existing works assumed deterministic load conditions. However, the deterministic design might have poor performance in practice when uncertainties exist. This article develops an efficient computational approach to robust concurrent topology optimization of macrostructure and material microstructure under single or multiple uncertain load cases.…”

Section: Introductionmentioning

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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Robust topology optimization for multiple fiber-reinforced plastic (FRP) composites under loading uncertainties

Cited by 48 publications

References 43 publications

Machine learning based topology optimization of fiber orientation for variable stiffness composite structures

Machine learning based topology optimization of fiber orientation for variable stiffness composite structures

Stacking sequences in composite laminates through design optimization

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

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