Numerical investigation of the asymptotic behavior of tape springs

• Autorzy: Coppedè Michele , Paroni Roberto , Picchi Scardaoni Marco

Identyfikatory

DOI

10.15632/jtam-pl/189814

• Języki publikacji: EN

Abstrakty

EN

Here, we investigate the behavior of the energy of a tape spring as its thickness becomes smaller and smaller. We consider the case of pure bending, i.e., we impose opposite rotations at both ends of the device. First, tape springs are introduced and their peculiar mechanical behavior is explained, and the details of the numerical model are carefully introduced. Then, a parametric study of the device is conducted for increasing end rotations and decreasing values of the thickness. Thus, we obtain parametric diagrams of reaction moments, energy per unit thickness, and energy densities. Finally, energy estimates are obtained.

Słowa kluczowe

EN

tape spring energy density; bending; elastic hinge; asymptotic behavior

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2024
• Tom: Vol. 62 nr 3
• Strony: 535--545
• Opis fizyczny: Bibliogr. 15 poz., rys.

Twórcy

autor

Coppedè Michele

• University of Pisa, Department of Civil and Industrial Engineering, Pisa, Italy

autor

Paroni Roberto

• University of Pisa, Department of Civil and Industrial Engineering, Pisa, Italy

autor

Picchi Scardaoni Marco

• University of Pisa, Department of Civil and Industrial Engineering, Pisa, Italy

Bibliografia

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• 2. Guinot F., Bourgeois S., Cochelin B., Blanchard L., 2012, A planar rod model with flexible thin-walled cross-sections. Application to the folding of tape springs, International Journal of Solids and Structures, 49, 1, 73-86.
• 3. Kumar A., Audoly B., Lestringant C., 2023, Asymptotic derivation of a higher-order one-dimensional model for tape springs, Philosophical Transactions of the Royal Society A, 381, 2244, 20220028.
• 4. Martin M., Bourgeois S., Cochelin B., Guinot F., 2020, Planar folding of shallow tape springs: the rod model with flexible cross-section revisited as a regularized Ericksen bar model, International Journal of Solids and Structures, 188, 189-209.
• 5. Picault E., Bourgeois S., Cochelin B., Guinot F., 2013, Un modèle de poutre à section mince flexible pour l’étude du comportement 3d des mètres rubans, Conference: 11e Colloque National en Calcul des Structures, Giens, France.
• 6. Picault E., Bourgeois S., Cochelin B., Guinot F., 2016, A rod model with thin-walled flexible cross-section: Extension to 3D motions and application to 3D foldings of tape springs, International Journal of Solids and Structures, 84, 64-81.
• 7. Picault E., Marone-Hitz P., Bourgeois S., Cochelin B., Guinot F., 2014, A planar rod model with flexible cross-section for the folding and the dynamic deployment of tape springs. Improvements and comparisons with experiments, International Journal of Solids and Structures, 51, 18, 3226-3238.
• 8. Riks E., 1972, The application of Newton’s method to the problem of elastic stability, Journal of Applied Mechanics, 39, 4, 1060-1065.
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• 10. Seffen K., 1997, Analysis of Structures Deployed by Tape-Springs, PhD Thesis, University of Cambridge.
• 11. Seffen K., Pellegrino S., 1999, Deployment dynamics of tape springs, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 455, 1983, 1003-1048.
• 12. Seffen K., You Z., Pellegrino S., 2000, Folding and deployment of curved tape springs, International Journal of Mechanical Sciences, 42, 10, 2055-2073.
• 13. Smith M., 2014, Abaqus/standard users manual, version 6.14-5, Simulia, Providence, RI.
• 14. Walker S.J., 2004, A Study of Three Dimensional Tape Spring Folds for Space Applications, PhD Thesis, University of Southampton.
• 15. Wempner G.A., 1971, Discrete approximations related to nonlinear theories of solids, International Journal of Solids and Structures, 7, 11, 1581-1599.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).