Isogeometric Analysis of Nonlinear Structural Vibrations

Abstract eng:
In this paper we analyze the vibrations of nonlinear structures by means of the novel approach of isogeometric finite elements. The fundamental idea of isogeometric finite elements is to apply the same functions, namely B-Splines and NURBS (Non-Uniform Rational B-Splines), for describing the geometry and for representing the numerical solution. In case of linear vibrational analysis, this approach has already been shown to possess substantial advantages over classical finite elements, and we extend it here to a nonlinear framework based on the harmonic balance principle. Using the nonlinear Euler-Bernoulli beam and rubber solids with frequency-dependent material properties as applications, we show that the isogeometric approach is a promising technique for the computation of nonlinear resonance frequencies and steady-state responses of structures described by geometrical or material nonlinearities. In particular, the higher smoothness of spline basis functions provides higher accuracy than polynomial-based finite elements.

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