## The side leg shape seat

Previously I discussed two design approaches, a tilted leg design and a straight leg design. These designs were very so, much different. The tilted legs showed some harmony on the design and looks great, the straight legs log resistant but no so much beautiful.

Today I will analyse the side leg shape seat.

From all this approach looks more stressed. The problem is that the table is supported by two legs instead of four plus it is taking all the torsional stresses generated by the table and weight. In regards to the design it looks that it will fall apart and challenges hour notion of safety. From all the designs this will be the most demanding regarding the material strengths.

Using a steel shaft unibody to support the upper seat table. The seat table is where we sit on. In order to make this type of approach it’s very important to use a very resistant material that will not break, can flex and is light weight. Not any wood could be used for this design since it is heavily stressed compared to the other two alternatives.

## Straight leg seat design for a bit of fun

Remembering when I was small, where i played countless hours with lego. Built many interesting constructions and tested the strength of many designs. That was a form of modeling the behaviour of a bridge, house or any structural  analysis that I could think of at that time. We all model things every day since we need to live in this world and figure out even if very basically the behaviour of objects. Think that when you hold an object you use the right force to hold it. Some how we know exactly the necessary configuration to execute physical task even without any though what so ever. When we look at a design and it challenges our notation that it will work it is because our underlaying protective system already is calculating and giving us feedback that it is dangerous to use. However this feeling can be wrong and the structure can be very safe, however most of the time our body is wright :).

I tested two designs on the simple table to understand what would happen.

This design present complete load transfer to the legs. The connection between table and leg is compress. Very little to none torsion is present. This design looks very stable, simple and is the classic, maybe the only simpler alternative is to use a solid cylinder instead, but that would make the seat very heavy. This design probably will hold as much as what the material used (wood, iron) can handle.

Comparing one design with another we can see that the behaviour to pressure  is completely different. The straight legs approach is stronger and would deal better with increased weight on top.

## Chair – Legs and IKEA

Yesterday I went to the mother of chairs and found so many design approaches that I got overwhelmed by it. It’s about purpose, function and creativity, ahh and some color.

Real examples of my previous figure were there! That was expected! I know….

Since I am a visual person I will show it any way… If you look closely 4 legs the central seat but pay attention to how the legs connect to the seat. This is the primary detail that holds everything together. Although materials change from metal to plastic, shaft diameter changes also but also important is how we consider this connection and how we simplify it. And which one will I study? It looks easier compared to the spider but not similar to the small table I shoed before.

Heres another shape.

Another design approach that has the advantage of folding.

Here the typical IKEA office chair. This chair can have different height levels.

The purpose of this post was to show there are many designs available and all of them try to solve a particular problem. There is no such thing as bad in any of the designs, maybe more a question of taste and function.

## So many types of things we can sit on

When we think of something to sit, we think on something we can rest on. These things are around since forever. However for the same function we have imagined a diverse set of designs that get things done. Every design has it’s advantages and disadvantages, probably material strength will play an important role here. The stronger the legs are the thiner they can be and more weight they can withstand. Bellow are a few representations os seats or tables (why not?) in 2D. Some imagination is important from here on. On my office I have I Rise Legs approach and a side legs design, on my living room I have a more classic straight legs design. Probably during a days work I will view many of these designs and probably you will too. Many reasons will determine the design from cost, function and requirements but I will be focusing on the open legs and straight leg variant. Differences? Maybe many, maybe not…. From intuition I feel that straight legs will be stronger but with 120 Kg on top….

## 4 leg chair the chalenge

Continuing my divagation through chair design and analysing the previous chair/seat post.

The purpose of this design is to serve as a support for objects. All 4 legs are tilted in a square fashion pattern at the bottom and are closer to each other near the table surface.

It’s not my intention to replicate the design of the table completely so my first simplification is the junction of the legs to the table.

Every design has it’s strengths and weaknesses. It’s purpose and function. This design is particularly sensitive to edge force since leg is supporting the table center. For a table this size the table will work comfortably with the objects we place on top, however as a seat considering an average weight of 80Kg.

So here starts the challenge:

• Withstand 80 Kg to 120Kg
• Use a clean, light design

Everyone probably already has an idea and the first one that comes up my mind is a straight leg chair (the simplest form of this design).

So why do we bother inventing new ideas??? The answer is that not all people are made equal. Some like simple chairs, others like edge design chairs, some others are in between and the rest probably don’t care.

Looking for over the edge designs, challenge our notion of possible or not possible. And maybe let us feel in some way better either for simplicity or because of blending in room design…

## Fracture Mechanics

I had an interesting problem to solve last week. It was concerning fatigue failure. A simple element after sucessive stress solicitations breaks apart (nothing new). It starts with a small scratch/crack and after a few million cycles and voilá the part breaks.

I initially made the traditional fatigue analysis but discovered that it is possible to go one step ahead! Using crack analysis directly in my model. Well I know this is around since at least 2014 so says Ansys.

My traditional approach involved a two way analysis where I calculated my maximum stresses for a dynamic input load measured through lab tests. After this I used standard fatigue analysis techniques to calculate the fatigue strenght. To do this I also required a wohler curve.

An alternative way is to include the crack into the finite element model and calculate what happens after a few cycles. Some software packages allow this type of calculation making our lives simpler.

I will go more indeph on fracture mechanics and fatigue in the future but for now I just want to give some good references to get started fast in this subject.

A good example of what to do, to give you a guide for your first steps on fracture mechanics can be seen in the following link.

https://caeai.com/resources/fracture-mechanics-workbench-v145-e-learning-presentation

A good example of a fatigue fracture can be seen in the Wikipedia

https://commons.wikimedia.org/wiki/File:Pedalarm_Bruch.jpg

https://en.wikipedia.org/wiki/Fatigue_(material)

https://en.wikipedia.org/wiki/Fatigue_(material)#The_S-N_curve

https://commons.wikimedia.org/wiki/File:Strain-N.png

## The meshing dilema uncovered

Finally I got the time to wrap up this subject and uncover this mystery. Actually none of the curves I presented was correct. Let me recap.

1. I used the default mesh – option 1,
2. I used a course mesh with general surface refinement – option 2
3. I used a bit finer mesh with local surface refinement – option 3

I got the above graph. Next I decided to cut the solid but shared the boundary conditions so that it was a single entity just sectioned. On my target edge/surface I defined a volume mesh (more refined) and on top of that near the edge I was studying and measuring I place a volume refinement. I got just about as much elements as before but now they were concentrated on my target zone.

The final mesh had the following

And the final result:

And here you go. The yellow curve has nothing to do with the blue curve which was my starting point and eventually converged with my previous 2 attempts.

Lessons learned:

Carefull usage of meshes, it is always good practice to verify mesh sensitivity. This example applies to any thing you do in simulation, it is always good to verify if the result we have in hand are actually trustable.

Comments to the starter: When ever your boss demands results immediately it is always tempting not to do a sensitivity analysis to rush and give something. If for instance this was a professional case (which it’s not) and one feed the blue line there would be some opportunity for mistakes. It is always important to verify how accurate a result the requester desires. On some clients the blue line would be wonderful for others it would be useless.

Ultimately the simulation result needs to fit the expectations of the requester. And the simulation effort, accuracy and time should fit those expectations.

## Tilted leg table curiosity

I spent a weekend at a Rock hotel. Well there was a lot of rock on the room, hallways, reception, everywhere! Well it’s a rock hotel! 🙂 The hotel was quite nice with a very good panoramic roof top with chill-out music (at least one place without rock in the hotel). On my room I noticed a table with tilted legs. I wondered if I sat on it, it would break.

The design is wonderful with black glass on top, however if I changed inclination of those legs even further would it break?  Could this design be used for a chair? Could I use 3 legs? could these legs be longer? These questions got in my mind.

## The meshing dilema

Some times we use the default mesh and get happy with the result,s others we don’t. It is hard to develop a test setup or expensive to buy the test setup equipment to calibrate the model. On these cases that we can’t compare results we have to take simulation results as final. This presents a few chalenges since how do we know the model is good enough for our purpose? Normally I follow two paths either by analytically calculating a rough value or by carefully analysing mesh sensitivty, analysing energy balances and whatnot. Although it is tempting to take a rough model as final, bad consequences can come from that decision, since we can end up with divergent results that relate more to model deficiencies than to the actual physics in hand.
Look at this example where I have 3 result set’s for varying thicknesses, however with different meshing strategies.

Which of the lines is the truth? Just a small change and such a big difference. You have to trust me on this, there is a big difference 200MPa from bottom blue to top grey.

## The mystery of the train seat uncovered

Will the train seat withstand 120Kg? was I seeing things? Maybe the weight was more since the person had a backpack. But the load was extreme.

I calculated 5 mm deformation on the cushion. Could I have seen it? Well maybe. Stresses were far away from the plasticity limit, however the structure feels loaded.

From my analysis the structure could take even more load and wobble even more. Maybe the squeaking sound over exaggerated my notion of wobbling.

The light blue image is the deformed state,  we can see the deformation direction, which moves in a expected direction.

In this close up we can see a slight displacement. But very small.

So my conclusions:

The heavy train traveller was safe, the seat could stand a few extra Kg’s of weight with some more camping equipment.

The design seems fairly robust, however it actually wobbles.