Increasing Cantilever Beam Stiffness

[Jeffrey Lee]

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.

 

[Nidum]

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 .

 

[Jeffrey Lee]

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!

 

[Nidum]

We can work out what you want from first principles if needs be but in general terms is this the sort of thing you have in mind ? :

http://waset.org/publications/10000410/design-and-development-of-constant-stress-composite-cantilever-beam

 

[Jeffrey Lee]

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.

 

[Nidum]

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 ?

 

[Jeffrey Lee]

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

 

[Nidum]

Jeffrey Lee - please contact me .