On approaches for avoiding low-stiffness regions in variable thickness sheet and homogenization-based topology optimization

Giele, Reinier; Groen, Jeroen; Aage, Niels; Andreasen, Casper Schousboe; Sigmund, Ole

doi:10.1007/s00158-021-02933-z

Cited by 17 publications

(17 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The design vectors are θ n , µ n and s, for orientation, widths, and material indication, respectively. The material indication is used for controlling the relative layering width [31], also detailed in Section 2.4. The optimization problem is defined as, min µ 1 ,...,µ N ,θ 1 ,...,θ N ,s…”

Section: Topology Optimization Problemmentioning

confidence: 99%

“…f * is the upper bound on of the allowed volume fraction of material in Ω . To make sure that the different optimization examples are comparable, the weighted compliance J is normalized by the compliance, J (0) , of a variable thickness sheet model with a uniform relative thickness of f * , (see [31] for more details). The orientation normalization value P (0) corresponds to θ n linearly changing from 0 to π from the lower-left corner of the design domain to the upper right.…”

Section: Topology Optimization Problemmentioning

confidence: 99%

“…Giele et al [31] observed that resulting topologies from homogenization-based topology optimization may consist of large regions of low-density material, which add a negligible benefit to the performance. This indicates that solutions are not well-defined and thus non-unique.…”

Section: Regularization Of Widthsmentioning

confidence: 99%

See 2 more Smart Citations

De-homogenization of optimal 2D topologies for multiple loading cases

Jensen

Sigmund

Groen

2022

Computer Methods in Applied Mechanics and Engineering

Self Cite

View full text Add to dashboard Cite

Section: Topology Optimization Problemmentioning

confidence: 99%

Section: Topology Optimization Problemmentioning

confidence: 99%

See 1 more Smart Citation

De-homogenization of optimal 2D topologies for multiple loading cases

Jensen

Sigmund

Groen

2022

Computer Methods in Applied Mechanics and Engineering

Self Cite

View full text Add to dashboard Cite

“…the work done by external forces, subject to a volume constraint. This objective is augmented by two additional terms; an angle regularization term F θ [17] and a penalization of the solid area [15]. The design variables are the two element-wise lamination parameters µ µ µ 1 , µ µ µ 2 , the angle θ θ θ, as well as an auxiliary material indicator field s.…”

Section: Optimization Problemmentioning

confidence: 99%

“…With this formulation, we ensure clear designs without non-physical lamination parameters in the interval [0, µ min [. For a detailed description of this approach, the readers are referred to the paper by Giele et al [15].…”

Section: Optimization Problemmentioning

confidence: 99%

De-homogenization using Convolutional Neural Networks

Elingaard,

Aage,

Bærentzen

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

This paper presents a deep learning-based de-homogenization method for structural compliance minimization. By using a convolutional neural network to parameterize the mapping from a set of lamination parameters on a coarse mesh to a one-scale design on a fine mesh, we avoid solving the least square problems associated with traditional de-homogenization approaches and save time correspondingly. To train the neural network, a two-step custom loss function has been developed which ensures a periodic output field that follows the local lamination orientations. A key feature of the proposed method is that the training is carried out without any use of or reference to the underlying structural optimization problem, which renders the proposed method robust and insensitive wrt. domain size, boundary conditions, and loading. A post-processing procedure utilizing a distance transform on the output field skeleton is used to project the desired lamination widths onto the output field while ensuring a predefined minimum length-scale and volume fraction. To demonstrate that the deep learning approach has excellent generalization properties, numerical examples are shown for several different load and boundary conditions. For an appropriate choice of parameters, the de-homogenized designs perform within 7 − 25% of the homogenization-based solution at a fraction of the computational cost. With several options for further improvements, the scheme may provide the basis for future interactive high-resolution topology optimization. Figure 1: De-homogenization of a 200 × 50 homogenization-based solution onto a fine mesh of 8000×2000 elements. Compliance of the de-homogenized design is within 17% of the homogenization solution, adheres to a predefined minimum relative thickness, and has been de-homogenized in just 15 seconds on a modern day laptop.

show abstract

Optimierungsgestützte Platzierung individueller Hohlkörper in Platten

Clauß,

Forman,

Rose

et al. 2023

Beton und Stahlbetonbau

View full text Add to dashboard Cite

Materialeinsparungen sind im Bauwesen unerlässlich. Ohne sie lassen sich die weltweit gesteckten Klimaziele nicht erreichen. Bei Betonplatten sind Hohlkörper eine Möglichkeit dazu. Sie verdrängen bis etwa 35 % an Betonvolumen, und zwar in Bereichen geringer Querkraft‐ und Biegebeanspruchung. Dabei wird bislang nur je eine Hohlkörperform eingesetzt. Im Beitrag wird ein Verfahren hergeleitet, das gegenüber den bisherigen Berechnungskonzepten zwei wesentliche Verbesserungen liefert. Zum einen sind beliebige Hohlkörperformen und ‐größen das Ergebnis, sodass innerhalb einer Platte je nach Tragfähigkeitsreserve verschieden große Hohlkörper nutzbar sind. Die Formen können beliebig rechteckig, kugelförmig oder ellipsoid ausfallen und werden generalisiert über sogenannte Superellipsoide beschrieben. Zum anderen ist die Optimierung an die Schnittgrößenermittlung der Platte gekoppelt, sodass die Veränderung der Schnittgrößenverteilung aus der Steifigkeitsbeeinflussung durch die Hohlkörper direkt ins Verfahren mit eingeht. Nachlaufende Kontrollen von Schnittgrößenumlagerungen entfallen. Kern des Optimierungsverfahrens ist die rechnerische Variation der Dichte, die mit dem verbliebenen Betonmaterial gleichgesetzt wird. Die Tragfähigkeit wird durch minimal einzuhaltende Druckzonenhöhen (Biegung) und reduzierte Widerstände schubunbewehrter Platten (Querkraft) nachgewiesen. Zwei Beispiele zeigen die praktische Anwendung an Plattenstreifen bzw. Flachdecken.

show abstract

On approaches for avoiding low-stiffness regions in variable thickness sheet and homogenization-based topology optimization

Cited by 17 publications

References 33 publications

De-homogenization of optimal 2D topologies for multiple loading cases

De-homogenization of optimal 2D topologies for multiple loading cases

De-homogenization using Convolutional Neural Networks

Optimierungsgestützte Platzierung individueller Hohlkörper in Platten

Contact Info

Product

Resources

About