team:gdeliege:nnm
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team:gdeliege:nnm [2015/08/13 10:57] – geoffrey | team:gdeliege:nnm [2016/03/30 15:23] (current) – external edit 127.0.0.1 | ||
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This is one of the research topics of the | This is one of the research topics of the | ||
[[http:// | [[http:// | ||
- | Actually, I knew nothing | + | Actually, I knew nothing |
told me about it | told me about it | ||
and about the nonlinear equations he wanted to solve with finite elements. | and about the nonlinear equations he wanted to solve with finite elements. | ||
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\end{eqnarray*} | \end{eqnarray*} | ||
$$ | $$ | ||
- | The domain boundary must be tangent to the velocity field to avoid problems with the definition of boundary conditions. Ludovic came up with clever and effective solutions to deal with this issue [2]. | + | The domain boundary must be tangent to the velocity field to avoid problems with the definition of boundary conditions. Ludovic came up with clever and effective solutions to deal with this issue [1]. |
+ | Fig. 1 shows results I obtained with my code for a simple 2-DOF system, also described in [1] | ||
+ | {{ : | ||
+ | //Figure 1. Finite element solution of a 2-DOF conservative system, calculated with my own code (mesh and visualization by [[http:// | ||
+ | |||
+ | I also attempted to solve a 6-DOF system corresponding to a cantilever beam. This requires the solution of a system of 10 equations with 10 unknown fields. | ||
+ | Although my code has been designed to allow the definition of an arbitrary number of unknown fields, I had never tried more than 2 or 3 fields coupled in one single formulation. The Jacobian matrix for the Newton-Raphson algorithm is written below; I wrote a Python script to define this formulation in my code avoiding copy-paste errors. | ||
+ | To my own surprise, it worked, although efficiency issues allowed me to solve the system on a small domain only. | ||
{{ : | {{ : | ||
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[1] L. Renson, G. Deliége, G. Kerschen. //An effective finite-element-based method for the computation of nonlinear normal modes of nonconservative systems.// Meccanica, vol. 49(8), pp. 1901-1916, 2014. \\ | [1] L. Renson, G. Deliége, G. Kerschen. //An effective finite-element-based method for the computation of nonlinear normal modes of nonconservative systems.// Meccanica, vol. 49(8), pp. 1901-1916, 2014. \\ | ||
[2] L. Renson. //Nonlinear Modal Analysis of Conservative and Nonconservative Aerospace Structures.// | [2] L. Renson. //Nonlinear Modal Analysis of Conservative and Nonconservative Aerospace Structures.// | ||
+ | \\ | ||
+ | [[team: | ||
team/gdeliege/nnm.1439456258.txt.gz · Last modified: 2016/03/30 15:22 (external edit)