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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. (Postprint)
In: Computer Methods in Applied Mechanics and Engineering, 345, Elsevier, ISSN 0045-7825,
DOI: 10.26083/tuprints-00019865,
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Item Type: Article
Origin: Secondary publication service
Status: Postprint
Title: Isogeometric shape optimization of nonlinear, curved 3D beams and beam structures
Language: English
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.

Journal or Publication Title: Computer Methods in Applied Mechanics and Engineering
Volume of the journal: 345
Publisher: Elsevier
Collation: 27 Seiten
Classification DDC: 600 Technik, Medizin, angewandte Wissenschaften > 600 Technik
600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften
Divisions: 16 Department of Mechanical Engineering > Cyber-Physical Simulation (CPS)
Date Deposited: 15 Dec 2021 13:48
Last Modified: 15 Dec 2021 13:49
DOI: 10.26083/tuprints-00019865
Corresponding Links:
URN: urn:nbn:de:tuda-tuprints-198653
Additional Information:

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

URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/19865
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