Thursday, June 30, 2005

Paper: PARTICLE SYSTEM APPROACH TO REAL TIME NON LINEAR ANALYSIS

  • Suitable for Real time analysis using a input, analysis, output loop
  • The time step is used to solve the differential equations of motion of a collection of particle masses.


What are the forces they consider:

  • Mechanical forces from distortion of connected elements
  • Viscous damping forces based on node velocity
  • Contact forces due to collision of surfaces
  • Forces spec as boundary conditions: applied loads etc

    How does the process work ?
    With the forces known on each node, acceleration is calculated. Then the velocity and position at the end of each time step can be calculated using numeric methods for ODEs. (Fourth order Runge Kutta method and an implicit trapezoid method)

    Insights for Claytronics
    One thing to realize here is that for our Claytronics , we don’t really need time steps as we are not considering motion right now. Its just a static analysis
    Second, the forces will be much simpler than described above, resulting in MUCH less computation and faster computation (probably tractable for catoms)

    Accuracy of this method
    The author applies it to two problems: beam with large displacements (max load bearable) and a double frame. The results match very well with theory and finite element analysis.

    Limitations
    Computationally intensive. But this paper analyzes dynamic situations, where movement is involved. In our case, it’s a case of analyzing static equilibrium , which is much simpler. They consider lot of dynamic forces and they have truss or beam elements which significantly complicate analysis.

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