Topology and thickness optimization of laminated composites including manufacturing constraints

Sørensen, Søren Nørgaard; Lund, Erik

doi:10.1007/s00158-013-0904-y

Cited by 82 publications

(60 citation statements)

References 26 publications

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“…In the preceding work by Sørensen and Lund (2013) it was, however, concluded that series of such straightforward constraints were insufficient at preventing so-called density bands where the topology variables settled on the same intermediate value throughout the thickness regardless of the penalization level. For this reason we apply the same modified constraints to prevent intermediate void as suggested in Sørensen and Lund (2013), thereby ensuring an acceptable transition between contiguous topology variables throughout the thickness. The constraints emerge systematically on basis of the sub-domain arrangement Ω dl followed by removal of repeated constraints because of potentially larger geometry domains ρ i .…”

Section: Preventing Intermediate Void (Mc4)mentioning

confidence: 99%

“…In Sørensen and Lund (2013), the threshold value T = 0.10 was found appropriate and is used in this work as well. Because the topology variable ρ 4 = 0 for the example in Fig.…”

Section: Preventing Intermediate Void (Mc4)mentioning

confidence: 99%

“…Previous work by Sørensen and Lund (2013) concluded that an SLP approach outperformed various Sequential Quadratic Programming (SQP) approaches, primarily due to the nature of the manufacturing constraints to prevent intermediate void through the laminate thickness, i.e., MC4 from (10). As this work includes the same challenging manufacturing constraints, we rely on an SLP approach once more, see for instance Arora (2004).…”

Section: The Slp Approachmentioning

confidence: 99%

“…Manufacturing constraints can furthermore be used to limit the complexity of the optimized design, thus making it possible to achieve a higher degree of manufacturability. In this work, four common manufacturing constraints, denoted MC1-MC4, introduced in the previous work by Sørensen and Lund (2013), are considered. MC1 is not an explicit constraint as it is related to the design parameterization.…”

Section: Introductionmentioning

confidence: 99%

“…The method proposed in this work is a continuation of the work by Sørensen and Lund (2013) who presented a novel method for simultaneous determination of material distribution and thickness variation of multilayered laminated composite structures. The preceding method was demonstrated on simply parameterized monolithic laminated plates with various boundary conditions, where the objective was to minimize compliance subject to a mass/volume constraint and manufacturing constraints MC1-MC4.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

DMTO – a method for Discrete Material and Thickness Optimization of laminated composite structures

Sørensen

Lund

2014

Struct Multidisc Optim

Self Cite

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Section: Preventing Intermediate Void (Mc4)mentioning

confidence: 99%

“…In Sørensen and Lund (2013), the threshold value T = 0.10 was found appropriate and is used in this work as well. Because the topology variable ρ 4 = 0 for the example in Fig.…”

Section: Preventing Intermediate Void (Mc4)mentioning

confidence: 99%

Section: The Slp Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

DMTO – a method for Discrete Material and Thickness Optimization of laminated composite structures

Sørensen

Lund

2014

Struct Multidisc Optim

Self Cite

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General topology optimization method with continuous and discrete orientation design using isoparametric projection

Nomura¹,

Dede²,

Lee

et al. 2014

Numerical Meth Engineering

121

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SummaryA general topology optimization method, which is capable of simultaneous design of density and orientation of anisotropic material, is proposed by introducing orientation design variables in addition to the density design variable. In this work, the Cartesian components of the orientation vector are utilized as the orientation design variables. The proposed method supports continuous orientation design, which is out of the scope of discrete material optimization approaches, as well as design using discrete angle sets. The advantage of this approach is that vector element representation is less likely to fail into local optima because it depends less on designs of former steps, especially compared with using the angle as a design variable (Continuous Fiber Angle Optimization) by providing a flexible path from one angle to another with relaxation of orientation design space. An additional advantage is that it is compatible with various projection or filtering methods such as sensitivity filters and density filters because it is free from unphysical bound or discontinuity such as the one at θ = 2π and θ = 0 seen with direct angle representation. One complication of Cartesian component representation is the point‐wise quadratic bound of the design variables; that is, each pair of element values has to reside in a given circular bound. To overcome this issue, we propose an isoparametric projection method, which transforms box bounds into circular bounds by a coordinate transformation with isoparametric shape functions without having the singular point that is seen at the origin with polar coordinate representation. A new topology optimization method is built by taking advantage of the aforementioned features and modern topology optimization techniques. Several numerical examples are provided to demonstrate its capability. Copyright © 2014 John Wiley & Sons, Ltd.

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A generalized discrete fiber angle optimization method for composite structures: Bipartite interpolation optimization

Zhang

Guo

Peng-wen

et al. 2022

Numerical Meth Engineering

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This paper proposes a novel fiber angle optimization method for composite, termed bipartite interpolation optimization (BIO), to address high‐dimensional design variables and inefficient fiber orientation optimization. The weighting functions of BIO are constructed with the help of multiphase material topology optimization approach. Various permutations and combinations of n design variables are utilized to represent 2n discrete candidate angles. Since the weighting functions of the way automatically satisfy the sum constraint, it is unnecessary to address the sum constraints during the optimization process. Compared with the traditional discrete material optimization strategy and solid isotropic material with penalization scheme, the BIO method reduces the dimension of the mathematical model for optimizing fiber angles. Compared to the shape functions with penalization scheme, the BIO method can be extended to the optimization problem of 2n candidates. Numerical examples of different types demonstrate that the proposed method has higher solution efficiency in the optimization problem of fiber orientation selection and is suitable for three‐dimensional shell optimization problems. It provides a new technical means for the structural optimization design of composite laminates.

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Topology and thickness optimization of laminated composites including manufacturing constraints

Cited by 82 publications

References 26 publications

DMTO – a method for Discrete Material and Thickness Optimization of laminated composite structures

DMTO – a method for Discrete Material and Thickness Optimization of laminated composite structures

General topology optimization method with continuous and discrete orientation design using isoparametric projection

A generalized discrete fiber angle optimization method for composite structures: Bipartite interpolation optimization

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