Nonlinear topology optimization of layered shell structures

Stegmann, Jan; Lund, Erik

doi:10.1007/s00158-004-0468-y

Cited by 27 publications

(13 citation statements)

References 19 publications

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“…There are five ways commonly use to represent a shell structure in the topology design of stiffeners (Lee et al 2000, Stegmann andLund 2005). They consist of the following five models, the: 1) Single-layer; 2) Double-layer; 3) Three-layer stiffening; 4) Three-layer voided; and 5) Multilayer-asymmetric.…”

Section: Layered Models For Shell Optimizationmentioning

confidence: 99%

“…The equation which represents the height z(x,y) of the spherical shell as a function of the x and y directions (Stegmann and Lund 2005) is given by Equation (8) and the design domain is shown in Figure 12a. The edge-length is L = 1000 mm, the height of the central point is h = 100 mm and the thickness is t = 60 mm.…”

Section: Corner Clamped Spherical Shell (Cap) With Square Platformmentioning

confidence: 99%

“…The stiffeners were placed at the locations of high strain energy/stress and material was removed from regions with small strain energy/stress. Stegmann and Lund (2005) investigated nonlinear effects of optimal stiffened topologies using the SIMP method (Bendsøe 1989). An anisotropic multi-layer shell model was employed to allow the formation of through-the-thickness holes or stiffening zones.…”

Section: Introductionmentioning

confidence: 99%

“…Three general observations can be made of these studies: 1) The contribution of the shell membrane was considered in the optimization (Lee et al 2000;Belblidia et al 2001;Stegmann and Lund 2005;Long et al 2009); 2) The optimization was carried out without the shell membrane (Gea and Fu 1997;Swam and Kosaka 1997;Luo and Gea 1998;Lam et al 2000;Suhuan and Zhijun 2005); and 3) Symmetry was forced when the stiffeners above and below the shell membrane were simultaneously optimized (Lee et al 2000;Belblidia et al 2001;Afonso et al 2005;Stegmann and Lund 2005).…”

Section: Introductionmentioning

confidence: 99%

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The effects of membrane thickness and asymmetry in the topology optimization of stiffeners for thin-shell structures

Victoria¹,

Querin²,

Díaz³

et al. 2013

Engineering Optimization

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ReuseUnless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version -refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher's website. TakedownIf you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. 1 The Effects of Membrane Thickness and Asymmetry in the Topology Optimization of Stiffeners for Thin Shell Structures Mariano Victoria Study into the Effects of Membrane Thickness and Asymmetry in the Topology Optimization of Stiffeners for Thin Shell StructuresThin walled shell structures are extensively used in architecture and engineering due to their lightweight and ease of shaping. But they suffer from poor overall stiffness, something addressed by the strategic addition of stiffeners. The optimization of stiffeners is divided between those which include shell membrane in the optimization and those which do not. However, no studies were found which indicate when it is necessary or valid to use either approach. In most cases it was also found that symmetry was forced in the optimization of stiffening layers. These two effects were investigated, concluding that: For membranes with thicknesses less than 20% of the structure, they do not affect the final topology; and for membrane thicknesses greater than 20%, they must be included in the optimization as they have a considerable effect. When bending and membrane loadings are present, symmetry should not be forced, otherwise sub-optimal designs are generated.

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Section: Layered Models For Shell Optimizationmentioning

confidence: 99%

Section: Corner Clamped Spherical Shell (Cap) With Square Platformmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The effects of membrane thickness and asymmetry in the topology optimization of stiffeners for thin-shell structures

Victoria¹,

Querin²,

Díaz³

et al. 2013

Engineering Optimization

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“…Choi et al 2000;Stegmann and Lund 2004;Uysal et al 2007;Kim et al 2013). It is easy and intuitive to describe a model geometry and to impose boundary conditions when the conventional FEM is used for a shell structure.…”

Section: Introductionmentioning

confidence: 99%

Isogeometric shape optimization of trimmed shell structures

Kang

Youn

2015

Struct Multidisc Optim

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In most of structural analyses and optimizations using the conventional isogeometric analysis, handling of trimmed or topologically complex geometries is difficult and awkward. A trimmed or topologically complex geometry is normally modeled with multiple untrimmed patches due to the tensor-product form of a Non-Uniform Rational B-Spline (NURBS) surface, and then the patches are put together for analysis. In the present work, the isogeometric shape optimization of trimmed shell structures using the information of trimmed NURBS surfaces is proposed. To treat the trimmed shell structures efficiently, two-dimensional Trimmed Surface Analysis (TSA) which is the isogeometric approach for treating a topologically complex geometry with a single patch is extended and adopted to the analysis and optimization of shell structures. Not only the coordinates of shell surface control points, but also the coordinates of trimming curve control points are chosen as design variables so that the curvatures of shell surface as well as the trimmed boundaries can be varied during the optimization. The degenerated shell based on Reissner-Mindlin theory is formulated with exact direction vectors and their analytic derivatives. Method of Moving Asymptotes (MMA) is used as the optimization algorithm, and the shape sensitivities with respect to the coordinates of surface control points and trimming curve control points are formulated with exact direction vectors and their analytic derivatives. The developed sensitivity formulations are validated by comparing with the results of Finite Difference Method (FDM), and they show excellent agreements. Numerical examples are treated to confirm the ability of the proposed approach.

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Aeroelastic topology optimization of membrane structures for micro air vehicles

Stanford

Ifju

2008

Struct Multidisc Optim

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Nonlinear topology optimization of layered shell structures

Cited by 27 publications

References 19 publications

The effects of membrane thickness and asymmetry in the topology optimization of stiffeners for thin-shell structures

The effects of membrane thickness and asymmetry in the topology optimization of stiffeners for thin-shell structures

Isogeometric shape optimization of trimmed shell structures

Aeroelastic topology optimization of membrane structures for micro air vehicles

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