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Isogeometric Analysis of Nonlinear Structural Vibrations

Bernd Simeon
TU Kaiserslautern


In this presentation, we consider Isogeometric Analysis for computing structural vibrations in the context of large deformation solids with nonlinear constitutive law. For linear vibrational analysis, the isogeometric approach has already been shown to possess advantages over classical finite elements and, in particular, pro- vides higher accuracy of the numerical results [1].

In our work, we introduce a nonlinear framework for isogeometric vibrational analysis based on steady-state frequency response to periodic excitations using the harmonic balance principle, which is then applied to 3-dimensional large deformation solids with visco-hyperelastic constitutive material models such as rubber. We demonstrate the method by means of computational examples and study the properties of the spatial discretization depending on polynomial degree and global smoothness. Furthermore, we aim at large-scale industrial applications where the naive application of harmonic balance is prohibitive. As remedy, a novel reduction scheme is proposed that leads to significant savings while maintaining sufficient accuracy for critical frequencies [2].

This work has been supported by the European Union within the FP7-project TERRIFIC: Towards Enhanced Integration of Design and Production in the Factory of the Future through Isogeometric Technologies.

[1] Cottrell, J.A.; Reali, A.; Bazilevs, Y.; Hughes, T.J.R.: Isogeometric analysis of structural vibrations. CMAME 195, 5257-5296 (2006)
[2] Weeger, O., Wever, U., Simeon, B.: Nonlinear frequency response analysis of structural vibrations. Computational Mechanics 54, 1477-1495 (2014)

Tuesday, February 24, 2015
11:00AM AP&M 2402