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A Comparison of Rotation-Free Triangular Shell Elements for Unstructured Meshes
KTH, School of Engineering Sciences (SCI), Mechanics.
KTH, School of Engineering Sciences (SCI), Mechanics.ORCID iD: 0000-0001-6802-8331
2007 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 196, no 49-52, 5001-5015 p.Article in journal (Refereed) Published
Abstract [en]

Many engineering applications require accurate and rapidly computed thin-shell elements. Rotation-free (RF) shell elements include the bending behaviour of thin shells without introducing any additional degrees of freedom compared to a membrane element. Instead, constant curvatures are approximated from the out-of-plane displacements of a patch of usually four triangular elements. A consequence of this is that the accuracy for irregular meshes has been unsatisfactory. The aim of this study is to find an RF shell element which is accurate also for unstructured meshes. The main difference between existing elements is whether they assume two-dimensional constant curvatures over the patch or use superposition of one-dimensional constant curvatures for the three pairs of triangles. The first assumption fulfils constant curvatures for a Kirchhoff plate exactly, whereas the second and most common assumption only approximates constant curvatures. The first assumption is significantly more resistant to element shape distortions, whereas the second assumption is slightly faster to compute and more appropriate on boundaries where one or more elements are missing or several neighbouring elements share a side. The combination is significantly more accurate for irregular meshes than other comparable RF elements for linear benchmark tests.

Place, publisher, year, edition, pages
2007. Vol. 196, no 49-52, 5001-5015 p.
Keyword [en]
shell element; rotation-free; constant curvatures; unstructured mesh
National Category
Engineering and Technology
URN: urn:nbn:se:kth:diva-9648DOI: 10.1016/j.cma.2007.06.017ISI: 000250494900014ScopusID: 2-s2.0-34548794751OAI: diva2:126806
QC 20100729Available from: 2008-11-21 Created: 2008-11-21 Last updated: 2010-11-08Bibliographically approved
In thesis
1. Deployment Control of Spinning Space Webs and Membranes
Open this publication in new window or tab >>Deployment Control of Spinning Space Webs and Membranes
2008 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

Future solar sail and solar power satellite missions require deployment of large and lightweight flexible structures in space. One option is to spin the assembly and use the centrifugal force for deployment, stiffening and stabilization. Some of the main advantages with spin deployment are that the significant forces are in the plane of rotation, a relatively simple control can be used and the tension in the membrane or web can be adjusted by the spin rate to meet the mission requirements. However, a successful deployment requires careful development of new control schemes. The deployment rate can be controlled by a torque, applied either to a satellite in the center or by thrusters in the corners, or by deployment rate control, obtained by tether, spool braking or folding properties.

Analytical models with only three degrees of freedom were here used to model the deployment of webs and membranes for various folding patterns and control schemes, with focus on space webs folded in star-like arms coiled around a center hub. The model was used to investigate control requirements and folding patterns and to obtain optimal control laws for centrifugal deployment. New control laws were derived from the optimal control results and previously presented control strategies. Analytical and finite element simulations indicate that the here developed control laws yield less oscillations, and most likely more robustness, than existing controls.

Rotation-free (RF) shell elements can be used to model inflation or centrifugal deployment of flexible memebrane structures by the finite element method. RF elements approximate the rotational degrees of freedom from the out-of-plane displacements of a patch of elements, and thus avoid common singularity problems for very thin shells. The performance of RF shell elements on unstructured grids is investigated in the last article of this thesis, and it is shown that a combination of existing RF elements performs well even for unstructured grids.

Place, publisher, year, edition, pages
Stockholm: KTH, 2008. x, 64 p.
Trita-MEK, ISSN 0348-467X ; 2008:10
Flexible structures, space webs, membranes, solar sails, solar power systems, deployment control, optimal control, centrifugal force deployment, spin deployment, rotation-free, shell elements
National Category
Engineering and Technology
urn:nbn:se:kth:diva-9574 (URN)
Public defence
2008-12-08, F3, KTH, Lindstedtsvägen 26, Stockholm, 10:00 (English)
QC 20100729Available from: 2008-11-21 Created: 2008-11-17 Last updated: 2010-07-29Bibliographically approved

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