FEA sim. - central-area axially-loaded cylinder

Purpose of this simulation

This is about examining how forces spread-out from a localised area-of-loading.
The body chosen is simple and axisymmetric, so physical principals maximally reveal themselves.

Why???

Stresses are not easy to image in a real body. They are difficult to reveal at a surface. (As far as I know) - there is no way to measure what the stress is at a given point within the volume of a 3-Dimensional body - thus to build up a map of stresses in a physical component.

Which makes it difficult to train the mind to visualise how forces spread-out and thus what the resultant stresses will be in a body...

So; here are my model results and I hope they are a useful start where there is a need to train the mind to visualise patterns of stresses.

Axisymmetric elements

A bonus of defining an axisymmetric situation and using axisymmetric elements ( previously encountered ) is very efficient of computing resources and number of elements and nodes used, enabling a fine mesh for the very detailed computation.

The model

The modelled situation, with the axisymmetric-elements FEA implementation with the FEA mesh.

The loads applied, and the average stresses resulting.

The Finite Element Analysis (FEA) program's model

Average case

The previous sketch-diagrams explained again in text and maths...

The body is 2m diameter (1m radius) and 2m long, of steel, with an axial tensile loading of 3142N.
As the area of a circular cross-section is Pi*r^2, so Pi*1*1=Pi, where Pi is 3.142,
that means the uniform stress would be 3142/3.142=1000Pa

That load of 3142N is applied over the middle half-diameter of the cylinder, so given the "squared" relationship to diameter, that area is 1/4 of the entire cylinder cross-sectional area.
So the stress at the area of load application tends to the average of 4000Pa.

The results

All exaggerated deformations are 1e7 times (10million times) the actual deformation.

What can be seen is - well, that is for you to interpret...

I observe

• the stress at the load-application areas tends to 4000Pa
• the stress at the mid-length remains highly non-uniform, with a higher-stressed core and lower stresses towards the surface; which appear to balance abount the average force/area value of 1000Pa
• although uniformity of stress is never achieved along this "short" cylinder, the forces do diffuse-outwards from the half-diameter end regions of application, progressively reducing the stress non-uniformity approaching the mid-length
• Poisson's Ratio effect pulls in the sides of the cylinder in the mid-length
• etc

Stress YY

(the local small high stress regions on the axis at the surfaces are likely an "artifact", produced by the approximations of the FEA model, but not representing anything in reality)

Displacement - Y

Displacement - X

Von Mises stress

(R. Smith, 13Jun2016)