A comparison between inverse form finding and shape optimization methods for anisotropic hyperelasticity in logarithmic strain space
Germain S, Steinmann P (2011)
Publication Language: English
Publication Type: Conference contribution
Publication year: 2011
Publisher: Wiley-VCH GmbH & Co.
City/Town: Weinheim
Book Volume: 7
Pages Range: 367-368
Edition: 1
Conference Proceedings Title: Proceedings of Applied Mathematics and Mechanics (PAMM)
Event location: Graz, Austria
Abstract
In this paper an inverse mechanical formulation and a Limited-Broyden-Flechter-Goldfarb-Shanno method for shape optimization are compared. Both methods deal with the determination of the undeformed shape of an hyperelastic part knowing its deformed configuration and the applied loads. We consider anisotropic hyperelastic materials that are formulated in the logarithmic strain space. Beside the theoretical aspects, we present a numerical example. We established that no difference could be found between the node coordinates on the undeformed sheets computed with both methods. However the convergence to the solution is faster for the inverse mechanical formulation compared to the L-BFGS algorithm.
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APA:
Germain, S., & Steinmann, P. (2011). A comparison between inverse form finding and shape optimization methods for anisotropic hyperelasticity in logarithmic strain space. In Proceedings of Applied Mathematics and Mechanics (PAMM) (pp. 367-368). Graz, Austria, AT: Weinheim: Wiley-VCH GmbH & Co..
MLA:
Germain, Sandrine, and Paul Steinmann. "A comparison between inverse form finding and shape optimization methods for anisotropic hyperelasticity in logarithmic strain space." Proceedings of the GAMM 2011, Graz, Austria Weinheim: Wiley-VCH GmbH & Co., 2011. 367-368.
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