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Increasing Cantilever Beam Stiffness

  1. Sep 24, 2015 #1
    Is it possible to create a cantilever beam with constant or increasing stiffness. I've been experimenting with several different shapes and profiles, and have not had any luck.

    I know that there are shapes with constant stress throughout, but I'm hoping to find a shape with constant or increasing stiffness, or the shape of a cantilever beam that has maximum stiffness throughout.
     
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  3. Sep 24, 2015 #2

    Nidum

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    There are many ways of making cantilever beams stiffer but any practical solution depends very much on what you are actually trying to do .

    What is basic requirement ?

    Leading dimensions and applied loads ?

    Class of job - basic plate and girder type construction or something more sophisticated ?

    Deflection limits ?

    Clear diagram would very useful .
     
  4. Sep 28, 2015 #3
    Hi, thanks for you reply. This is for applications in the prosthetics field, so geometry and construction is dependent upon what can be contained within a biological form factor.

    Basic dimensions:
    Cross Section: 6 x 25 mm
    Length: 100 mm

    Material:
    Carbon Fiber with E = 3.8E10 Pa

    Maximum applied load is around 1200 N

    Attached is a picture of the general setup, please let me know if you have any other questions.

    Thanks!
     

    Attached Files:

  5. Sep 28, 2015 #4

    Nidum

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  6. Sep 28, 2015 #5
    Somewhat, but that is designing for constant stress. I am hoping to find the optimum shape for stiffness. What I have been trying to do is using the equations for angular deflection, vertical displacement in order to find a shape that maximizes stiffness (F/displacement). These are the equations I have been using.

    $$\theta (x) = \frac{1}{E} \int \frac{M(x)}{I(x)} dx$$
    $$\delta (x) = \int \theta(x) dx$$

    I have varied the equation for I(x) based on different profiles, but am wondering what the optimal shape for k(x) would be.
     
  7. Sep 28, 2015 #6

    Nidum

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    Maximum stiffness as such is open ended - for a simple parallel or tapering down cantilever beam the deeper the sections used the stiffer it gets .

    Need some constraints for a meaningful analysis .

    Would it be useful for your purpose if we try to find shape of a cantilever beam with best stiffness compared to stiffness of your existing parallel one and using same amount of material ?
     
    Last edited: Sep 28, 2015
  8. Sep 28, 2015 #7
    Yes, that would be helpful. Finding the max stiffness of a cantilever beam at its tip with the same amount of material, and both being the same length would be of use to me.

    Thank you
     
  9. Oct 12, 2015 #8

    Nidum

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    Jeffrey Lee - please contact me .
     
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