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Isogeometric shape optimization of nonlinear, curved 3D beams and beam structures

Weeger, Oliver ; Narayanan, Bharath ; Dunn, Martin L. (2021)
Isogeometric shape optimization of nonlinear, curved 3D beams and beam structures.
In: Computer Methods in Applied Mechanics and Engineering, 2019, 345
doi: 10.26083/tuprints-00019865
Article, Secondary publication, Postprint

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Item Type: Article
Type of entry: Secondary publication
Title: Isogeometric shape optimization of nonlinear, curved 3D beams and beam structures
Language: English
Date: 2021
Place of Publication: Darmstadt
Year of primary publication: 2019
Publisher: Elsevier
Journal or Publication Title: Computer Methods in Applied Mechanics and Engineering
Volume of the journal: 345
Collation: 27 Seiten
DOI: 10.26083/tuprints-00019865
Corresponding Links:
Origin: Secondary publication service
Abstract:

Straight beams, rods and trusses are common elements in structural and mechanical engineering, but recent advances in additive manufacturing now also enable efficient freeform fabrication of curved, deformable beams and beam structures, such as microstructures, metamaterials and conformal lattices. To exploit this new design freedom for applications with nonlinear mechanical behavior, we introduce an isogeometric method for shape optimization of curved 3D beams and beam structures. The geometrically exact Cosserat rod theory is used to model nonlinear 3D beams subject to large deformations and rotations. The initial and current geometry are parameterized in terms of NURBS curves describing the beam centerline and an isogeometric collocation approach is used to discretize the strong form of the balance equations. Then, a nonlinear optimization problem is formulated in order to optimize the positions of the control points of the NURBS curve that describes the beam centerline, i.e., the geometry or shape of the beam. To solve the design problem using gradient-based algorithms, we introduce semi-analytical, inconsistent analytical and fully analytical approaches for calculation of design sensitivities. The methods are numerically validated and their performance is investigated, before the applicability and versatility of our 3D beam shape optimization method is illustrated in various numerical applications, including optimization of an auxetic 3D metamaterial.

Status: Postprint
URN: urn:nbn:de:tuda-tuprints-198653
Additional Information:

Isogeometric analysis, Collocation method, Shape optimization, Nonlinear optimization, 3D beams, Geometrically exact beam theory

Classification DDC: 600 Technology, medicine, applied sciences > 600 Technology
600 Technology, medicine, applied sciences > 620 Engineering and machine engineering
Divisions: 16 Department of Mechanical Engineering > Cyber-Physical Simulation (CPS)
Date Deposited: 15 Dec 2021 13:48
Last Modified: 15 Aug 2023 07:16
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/19865
PPN: 510610471
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