On the behaviour of the ANM continuation in the presence of bifurcations

By S. Baguet, Bruno Cochelin. 2003

59 citations recorded by the source corpus.

The asymptotic-numerical method (ANM) is a path following technique which is based on high order power series expansions. In this paper, we analyse its behaviour when it is applied to the continuation of a branch with bifurcation points. We show that when the starting point of the continuation is near a bifurcation, the radius of convergence of the power series is exactly the distance from the starting point to the bifurcation. This leads to an accumulation of small steps around the bifurcation point. This phenomenon is related to the presence of inevitable imperfections in the FE models. We also explain that, depending on the maximal tolerated residual error (out-of-balance error), the ANM continuation may continue to follow the fundamental path or it may turn onto the bifurcated path without applying any branch switching technique.

Subfields: Computational Theory and Mathematics, Electrical and Electronic Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/32e337b431f9be0c6a2aaeb871b9889c88eb17be

How researchers see this paper

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In Computational Theory and Mathematics

1. Bruno Cochelin
2. Ludovic Renson
3. Gaetan Kerschen

In Electrical and Electronic Engineering

1. Bruno Cochelin
2. Ludovic Renson
3. Gaetan Kerschen

In Numerical Analysis

1. Ludovic Renson
2. Gaetan Kerschen
3. Bruno Cochelin

Citations in the corpus

• Numerical computation of nonlinear normal modes in mechanical engineering (2016, background): “The validity interval [0, smax] inside which the series satisfies ‖H(U(s))‖ ≤ ǫr with ǫr a prescribed tolerance can be defined as [62]:”