Finite Element Analysis

(fillet weld with toe-groove)

Answering a reasonable question: what is Finite Element Analysis?

The start of the 2016 endeavour...

Reading the principles of Finite Element Analysis (FEA) had always spiked my hair back horizontally, for negligible retention.
It's a learning style issue. I've tried reading mathematics books on mathematical methods I have "reinvented" independently and I can't understand a word the book says.

So I came to the idea that I should play around with a FEA package, letting the "tool" do its thing, then let the accumulating observations and interest draw me towards the theory.
That also matches my path to now, as a practical learner.
Be aware though that my practical and playing-around approach can make me an innovator. I have broken new ground in science and engineering. Just in case anyone thought the approach is "lesser".
Support for this view came from an interesting 11 minute "YouTube" video of a mathematician Gilbert Strang expounding his thoughts and perceptions on the Finite Element method ("Finite element method - Gilbert Strang").
He describes Finite Element Analysis as being the biggest dispersed teamwork endeavour in human history, with progress flowing back and forth between engineers, mathematicians, computer scientists and others (8min 05s on video). Incrementally feeling their way forwards, finding their way, staging by useful intermediate goals.
So the human picture is no one human ever went in possessing a comprehensive forward view.
Therefore, it seems reasonable that I should not expect myself to have go in guided by a comprehensive forward view...!

My Web search and read on FEA had an encouraging message; the FEA I wanted to achieve, stresses in structures, is the simplest case of FEA.
The solution is static (you put a load on and the structure takes up a stressed state; you come along and deduce what that unvarying stressed state is).
It's linear-elastic because of the application (for structures, you generally don't want the structure deforming; therefore stresses for eg a bridge should be in the elastic range - whereas deformation introduces non-linear behaviour which can now be modelled but is an extra sophistication)

[ Personal backdrop to this endeavour studying FEA]

So I felt ready to go...

First action - download LISA FEA

The tutorials for LISA FEA ( LISA website , see tutorials ) chimed-in right for me. Explanations were simple. Emphasis on nodes and elements, getting them in place to make early progress on projects, seemed promising for the "get started somewhere" approach I visualised.

LISA FEA is not "free software"; but the limited version capped at 1300 nodes is free. I'll see where I go onwards later...

My first ever FEA simulation!

I followed the first LISA FEA tutorial ("Tutorials -> Analysis types -> Static").
It worked! So I'd got an installed FEA program and could broadly get it to respond.

My first ever FEA simulation (precious only to me, for sure!)

Next - have a go at stress-fields around T-fillet welds

In 2011 I did research on fatigue-resistant T-fillet welds, for naval and structural applications.
eg shown in this webpage

Could I now model those welds?

Here is where I had a go....

"Crack tip stress-field" simulations

I tried modelling the stress-concentration field around the tip of a crack.
In any practical sense that's totally inadvisable.
However, it produces pretty pictures and the actual stress-fields are known from engineering investigation trying to avoid fracture of components. So you can kind-of get some idea of how well you are doing...

Modelling of stresses in a cracked sample

Simulation of fillet-weld "toe" with specific weld features

As previously mentioned, I've done a research programme on fatigue-resistant welds. That went to some detail; including metallography of the weld toe showing early-stage fatigue-cracking.

Those findings in 2011 were controvertial.
With developing ability at applying the FEA computational tool, could I now perform FEA simulations providing useful explanation of those observed outcomes?

I'm applying planes-of-symmetry to FEA solutions by this stage.

Here is the outcome: simulations of fillet-welds with different weld-toe features .

Pressure-vessels - getting into engineering...

This programme of work is learning how to use shell-elements to build models of pressure-vessels

Reminding readers that this is early-stage work, and there is a high chance of "a well of sense in an abyss of stupidity" (!!!) errors.
So these "results" should not be taken too literally.

The LISA FEA tutorial

Copied the tutorial - it worked. No pictures taken.

Spherical pressure vessel

Putting hemispherical ends on a cylindrical pressure vessel would have produced more than one challenge at once. The single-step next challenge was therefore a spherical pressure vessel like a Horton sphere , as seen at petrochemical refineries.

My spherical pressure vessel simulation.

Very simple cylindrical pressure vessel (no ends!)

Quick check of some fundamentals, with this simple cylindrical vessel simulation.

Hemispherical-ended cylindrical pressure vessel simulation

Hemispherical-ended cylindrical pressure vessels are used in real applications.
The stresses in the cylindrical body should be different from that of the hemispherical ends; so the output is anticipated with interest

My simulation of a hemispherical-ended cylindrical pressure vessel .

Axisymmetric FEA simulations

A couple of FEA simulations applying axisymmetric elements .

Line elements for beam / column and lattice structures

Line-elements enable simulation of structures with a lot of space in-between structural components which are long and of constant cross-section.

Simple "beam" line-element simulations

Some initial simple "practice" "beam" line-element simulations .

Truss structures simulated with linear elements

These modelled lattice-structures representing truss-bridges are simulated using line-elements.

Warren-truss and Vierendeel-truss .

Going beyond the first calendar-month!!!

Beyond here is breaking-out beyond what fitted in a calendar month from first downloading a Finite Element Analysis program and giving it a try...
Comment on the backdrop to that first month.
My onwards efforts...

Mixed line-element and shell-element FEA model

My mixed line-element and shell-element FEA model

Orthotropic bridge deck FEA model

My orthotropic bridge deck FEA model

Stress profile visualisation in a centrally-loaded cylinder

This is an "underlying science" / "engineering fundamentals" exercise.
A significant application of FEA is visualising the non-uniform stress distributions associated with features of the physical object.
Here is stress distribution in a simple centrally-loaded cylinder ; as an exercise in thinking about how stresses distribute in a body.

Another in this series; double the length, at 4m . Diameter and loading condition stay the same.

Comparing Warren and Vierendeel truss performance by FEA modelling

These Warren-truss and Vierendeel-truss simulations are identical in every aspect apart from being different types of truss.

This presentation is a new departure, as I am now inviting engineering comparative evaluation of the merits of different structures on the basis of Finite Element Analysis models of them which I have done.

Comparing otherwise-identical Warren and Vierendeel Truss models .

End of initial programme - the summary

I've summarised the outcome of this, my initial Finite Element Analysis endeavour.
At this juncture, it looks that the way ahead is a new different programme of work, of a different character, starting a new chapter.

I hope you have enjoyed sharing my initial Finite Element Analysis modelling and simulations experiences.

(R. Smith, 17May2016, frequent updates to 02June2016, 06June2016, 14June2016, 16June2016)