Increasing Cantilever Beam Stiffness

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Discussion Overview

The discussion centers on the design of cantilever beams with the goal of achieving constant or increasing stiffness, particularly in the context of applications in prosthetics. Participants explore various shapes and profiles, mathematical equations related to deflection and stiffness, and the constraints that influence design choices.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant inquires about the possibility of creating a cantilever beam with constant or increasing stiffness and mentions experimenting with different shapes.
  • Another participant suggests that practical solutions for increasing stiffness depend on specific requirements such as dimensions, applied loads, and deflection limits.
  • A participant specifies the application in prosthetics, providing dimensions and material properties, and requests further input based on these constraints.
  • Discussion includes references to existing designs focused on constant stress rather than stiffness optimization.
  • One participant expresses interest in using equations for angular deflection and vertical displacement to find an optimal shape for stiffness.
  • Another participant notes that maximum stiffness is open-ended and suggests that deeper sections in a cantilever beam increase stiffness, while also requesting constraints for meaningful analysis.
  • There is a request for assistance in finding the maximum stiffness of a cantilever beam at its tip while maintaining the same amount of material and length.

Areas of Agreement / Disagreement

Participants express varying views on the approach to maximizing stiffness, with some focusing on constant stress designs and others on optimizing shapes for stiffness. The discussion remains unresolved regarding the best method to achieve the desired beam characteristics.

Contextual Notes

Participants mention the need for constraints and specific requirements to conduct meaningful analyses, indicating that the discussion is dependent on various assumptions and definitions related to beam design.

Jeffrey Lee
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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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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 .
 
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!
 

Attachments

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
 
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.
 
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:
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
 
Jeffrey Lee - please contact me .
 

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