Metafor

ULiege - Aerospace & Mechanical Engineering

User Tools

Site Tools


team:gdeliege:nnm

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revisionPrevious revision
Next revision
Previous revision
team:gdeliege:nnm [2015/08/13 10:57] geoffreyteam:gdeliege:nnm [2016/03/30 15:23] (current) – external edit 127.0.0.1
Line 6: Line 6:
 This is one of the research topics of the  This is one of the research topics of the 
 [[http://www.ltas-s3l.ulg.ac.be/cmsms/|Space Structures & Systems Lab.]] (Prof. Kerschen). [[http://www.ltas-s3l.ulg.ac.be/cmsms/|Space Structures & Systems Lab.]] (Prof. Kerschen).
-Actually, I knew nothing on the subject until Ludovic Renson+Actually, I knew nothing of the subject until Ludovic Renson
 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.
Line 54: Line 54:
 \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]
  
 +{{ :team:gdeliege:nnm02.png |}}
 +//Figure 1. Finite element solution of a 2-DOF conservative system, calculated with my own code (mesh and visualization by [[http://www.geuz.org/gmsh|Gmsh]]): (1) mesh of the elliptical domain, (2) pseudo-velocity field, (3) displacement $X2$, (4) velocity $Y2$.//
 +
 +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.
 {{ :team:gdeliege:nnm01.png |}} {{ :team:gdeliege:nnm01.png |}}
  
Line 62: Line 69:
 [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.// PhD Thesis, Université de Liège, 2014. \\ [2] L. Renson. //Nonlinear Modal Analysis of Conservative and Nonconservative Aerospace Structures.// PhD Thesis, Université de Liège, 2014. \\
 +\\
 +[[team:gdeliege|Back to main page]]
  
  
team/gdeliege/nnm.1439456258.txt.gz · Last modified: 2016/03/30 15:22 (external edit)

Donate Powered by PHP Valid HTML5 Valid CSS Driven by DokuWiki