I am a mechanical an engineer with 2

[jball1]

I am a mechanical an engineer with a few years of experience. Most of the work I do is transient, structural finite element analysis. I have gotten reasonably competent at building models and pumping out results, but I regularly come across gaps in my fundamental knowledge. I have been doing some reading on the basics of finite element analysis because I want to understand more of its mathematical foundations.
My understanding is that the finite element method is often (primarily?) used to solve partial differential equations, which get pretty hairy. In structural analysis, the fundamental equation I am solving is the Equation of Motion:

F=ma+cv+kx

This is an ordinary differential equation, not a PDE. Are PDE's involved in structural analysis?

 

[FEA way]

Here are the PDE’s solved in FEA (equations of linear elasticity theory):

Source:

https://en.m.wikipedia.org/wiki/Linear_elasticity

 

[rb1957]

actually I think FEA is solving for least work using Castigliano's method …

https://en.wikipedia.org/wiki/Castigliano's_method

https://interestingengineering.com/what-is-finite-element-analysis-and-how-does-it-work

it is scary that people are using tools they don't understand, but kudos for trying to learn. There are lots of online references that'll help.

another day in paradise, or is paradise one day closer ?

 

[IceBreakerSours]

I will sacrifice precision to get the basic idea across with minimal effort so please take the rest with a pinch of salt.

You assume an idealized mathematical model of reality with rigid masses, springs, and dashpots and by balancing out the forces you find your equation of motion which ends up being an ODE. As powerful as that ODE is, it is not terribly general because, well, you don't see a lot of idealized rigid bodies around, do you? That is where continuum mechanics kicks in and the simple ODE turns into a PDE which says the forces in a deformable domain are balanced in space and time - pointwise. That is a general and, therefore, very powerful statement. Since there are multiple domain variables involved (x, y, z, and t), you have to solve a partial DE. Now, since digital hardware cannot do calculus, you discretize the space using finite elements and time using implicit or explicit time integration and turn the calculus problem into a linear algebra problem (Ax=b).

You can spend years trying to understand FEA which would not be terribly productive so you have to choose your perspective (fundamental math, linear algebra, structural dynamics?) and goals (good feel, being able to test elements/materials, writing your own simple code, etc.). One of the easiest and quickest introductory lecture notes are by Scott Hollister here. The next level is on solidmechanics.org. From there you can go to Klaus-Jurgen Bathe's lecture videos on YouTube for linear and nonlinear FEA.

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[FEA way]

There are various approaches in FEA, including the one using the principal of virtual work or the one using weak form of aforementioned equations of motion. Check, for example, the paragraph "Weak form of equilibrium equations - three-dimensional case" in the book titled "Introduction to the Finite Element Method" by Ottosen.


"it is scary that people are using tools they don't understand, but kudos for trying to learn." I agree with that

 

[jball1]

Thanks all for taking the time to respond. Believe it or not, I have taken grad level classes on FEM. However, I am the kind of person that tends to get really good grades in classes, but then sometimes I can't remember even the fundamentals of the course after a year or two. This is embarrassing... but it is the truth.

I am a few years into my career, and I have found that I actually seem to retain things best when I write them out, long-form, in my own words. I find that if I can't explain something in detail, I don't really understand it. I then am able to go back about once a year to refresh my understanding. So basically, I have been creating my own mini-textbooks for subjects which relate to the work that I do.

This is very slow going, but I am in no hurry - I believe I will be in my current role as an analyst until I retire. So I have actually gone all the way back to differential equations and linear algebra (using Schaum's textbooks as a guide, which I believe were recommended somewhere on eng-tips). I am hoping to finish those two mid next year, and then I'll work up from that foundation into Solid Mechanics, FEM, etc. So I am getting a little ahead of myself here asking a FEM question, but this is a question that has been in my mind for a while.

Anyways, I know there is plenty of information online, and I take advantage of this often. But every once in a while, I find it very helpful to ask a very specific question in my own words.

Thanks again for the help. I am sure I will be back, periodically.

 

[jball1]

it is scary that people are using tools they don't understand, but kudos for trying to learn. There are lots of online references that'll help.

Yeah, to be honest, I am embarrassed by this, but I feel better because

[ol 1]
[li]I know that time is on my side. As I said in the prior post, I believe I will be in my current role until I retire (love the work, love the company, and adequate compensation). I believe you can learn just about anything if you are patient and put in the work. I also find that the more complicated something is, the more rewarding it is to learn. And maybe it isn't for you, but I find solid mechanics and FEM to be pretty complicated stuff!

[/li]

[li]I find that many of my peers (young engineers) are in a similar position (no strong grasp of the fundamentals)
[/li]
[/ol]

 

[jball1]

I will sacrifice precision to get the basic idea across with minimal effort so please take the rest with a pinch of salt.

You assume an idealized mathematical model of reality with rigid masses, springs, and dashpots and by balancing out the forces you find your equation of motion which ends up being an ODE. As powerful as that ODE is, it is not terribly general because, well, you don't see a lot of idealized rigid bodies around, do you? That is where continuum mechanics kicks in and the simple ODE turns into a PDE which says the forces in a deformable domain are balanced in space and time - pointwise. That is a general and, therefore, very powerful statement. Since there are multiple domain variables involved (x, y, z, and t), you have to solve a partial DE. Now, since digital hardware cannot do calculus, you discretize the space using finite elements and time using implicit or explicit time integration and turn the calculus problem into a linear algebra problem (Ax=b).

You can spend years trying to understand FEA which would not be terribly productive so you have to choose your perspective (fundamental math, linear algebra, structural dynamics?) and goals (good feel, being able to test elements/materials, writing your own simple code, etc.). One of the easiest and quickest introductory lecture notes are by Scott Hollister here. The next level is on solidmechanics.org. From there you can go to Klaus-Jurgen Bathe's lecture videos on YouTube for linear and nonlinear FEA.

Thank you. I found this to be a really concise, really understandable answer.

 

[jball1]

Also... is there any way for me to change the title of this thread? Somehow I left out the title originally. No worries if there isn't, but it probably will be less helpful to others without an appropriate title.

 

[rb1957]

Maybe you can ask the mgmt. … RF your post, and ask to change the subject line.

another day in paradise, or is paradise one day closer ?

 

[jball1]

You can spend years trying to understand FEA which would not be terribly productive so you have to choose your perspective (fundamental math, linear algebra, structural dynamics?) and goals (good feel, being able to test elements/materials, writing your own simple code, etc.).

Agreed. My goals are:
[ol 1]
[li]To be given more complicated work. I work for a large-ish company that has several hundred people who do analysis. Of those analysts, only ~100 of us do analysis full time. Of the 100 full-time analysts, maybe 3/4 are doing analysis work that is largely "following a recipe", supporting production. That's not entirely fair, it's not like they don't run into complicated problems that need higher level engineering to resolve. But there is always pressure to quickly move past issues, since their work is tied to production. This isn't a knock against our company, I think just about every company feels this tension. Overall, I think our company does a reasonable job dealing with it, but the pressure to move faster, reach a conclusion, etc is always there.

The other 1/4 of the full time analysts get to solve the truly thorny problems that come up, as well as developing some of the software that we use. Their work is much more physics based, rather than recipe based. They are given the luxury of time to delve into whether or not their models accurately represent the involved physics, rather than tending to simply crank out results based upon established rules.

I want to move from the first group to the second. I have demonstrated that I work hard, and that I am willing and able to learn, but I don't yet have the technical chops to do much of the work done in the second group.

[/li]

[li]Develop expertise in the areas of solid mechanics and FEM, simply because developing expertise is rewarding
[/li]
[/ol]

 

[rb1957]

you are very lucky to have found such a great fit to yourself !

There are plenty of online resources for the study of FEA. That and practise with models (real structures and possibly more importantly test models) will get you a long way.

Someone (a mentor) to talk to will also help.

Get that under your beat before going on any training courses.

good luck !

another day in paradise, or is paradise one day closer ?

 

[IceBreakerSours]

I applaud you for having this level of maturity and having a sense for what you want realistically. I agree 100% with the previous comment: You really want to have a mentor.

While working in group two offers advantages for your taste, there are some disadvantages that you may not be appreciating: You will be distant from the product and will lose some degree of control of the flow of information, you will not have as many relationships in the projects, the funding mechanism will be different so the projects you get to work on may not necessarily be as "exciting" because, for example, they may not have immediate impact, you may not get as much credit, etc. I suggest you have another mentor from that group before you make efforts to move to that group.

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[IRstuff]

Sounds like you need to get cozy with one of the 1/4 and try to get some overflow work from them, particularly stuff that they might not be that gung-ho to do themselves.

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert!

https://www.youtube.com/watch?v=BKorP55Aqvg

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[jball1]

While working in group two offers advantages for your taste, there are some disadvantages that you may not be appreciating: You will be distant from the product and will lose some degree of control of the flow of information, you will not have as many relationships in the projects, the funding mechanism will be different so the projects you get to work on may not necessarily be as "exciting" because, for example, they may not have immediate impact, you may not get as much credit, etc.

I think everything you say here is true. There are a few disgruntled employees in the group I am aiming to join, and now that I think about it, it is likely for some of the reasons you mention. Some of them have had projects cancelled after years of working on them, just because there is a new director in town and he/she no longer finds the project useful/interesting. And in some cases, this seems to have lead to bitterness, lack of motivation.

Also, as you mention, there will be fewer relationships. In the larger group, we function sort of as consultants to other structural and mechanical engineers. They own the products, and we ensure that their designs meet certain requirements. I have enjoyed many of the relationships I have built in this role. In the second group, I will be much more isolated.

So these are definitely risks. However, without going into a bunch more detail that would probably bore everyone, I think the rewards outweigh the risks.

Sounds like you need to get cozy with one of the 1/4 and try to get some overflow work from them, particularly stuff that they might not be that gung-ho to do themselves.

I have actually done this. Our company is about to start a very large project (will take decades to complete). Our department has gotten significant R&D money to develop new capabilities in support of this project. Apparently we haven't seen money like this for 15+ years. The guy leading the effort from our department is someone I get along with very well. He actually was formerly in the same group I am in, and was my mentor when I started. Then he got a PhD and moved to the other group. I recently strongly considered pursuing a PhD, but decided against it. In the process of evaluating that path, I reconnected with my former mentor.

I expressed interest in doing work for him, and he passed of a project to me, and basically told me I could work on whatever I want to related to his project (at the moment, they are very understaffed). The trick is figuring out how to get the work done alongside my other responsibilities. Thankfully, I have a really good relationship with my actual boss, and he is fully aware that I may eventually make the transfer.

 

[human909]

This is a good question with some good answers.

The answer I didn't like was this one:

it is scary that people are using tools they don't understand

WE ALL use tools that we don't understand! In fact we are all using tools now that we don't understand. Think of all the different processes/protocols/calculations/etc.. being used just to enable me to type this message. No single person has a full grasp of every process in this chain. The world is full of countless examples, in fact this specialization is what has brought us from the stone age to the information age.

You don't need to know the deep inner workings of a tool (FEA) to be able to be an effective user of it.

 

[IRstuff]

You don't need to know the deep inner workings of a tool (FEA) to be able to be an effective user of it.

True, but you do need to know when it's giving you silly answers ;-)

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert!

https://www.youtube.com/watch?v=BKorP55Aqvg

faq731-376 forum1529 Entire Forum list

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[IceBreakerSours]

I find that answer fine because its not just any tool. If you do not understand the one tool that brings you bread and could bring great harm to others if not used appropriately, then that is a problem.

I have heard that if you haven't coded it, you do not understand it. Sure, I get that but, by that logic, my response is that "no one understands FEA" in the sense that even coders at all major commercial vendors are focused on their little piece of the puzzle. Also, it has been documented many times over that code has bugs (every 50 lines or so, there is a bug!) so developers ought to have some humility too. Finally, it is not uncommon to see tech support guys outperform developers in coming up with solutions for customers. I can go on and on.

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[IceBreakerSours]

I want to add another thought -

To make yourself valuable to the group you want to land yourself in, there may be other skills you can bring to the table. Few computational analysts are also trained in probabalistic methods so you could explore that avenue; they bring another layer of rigor to analysis. There is a ton of content available online if you wish to train yourself (DAKOTA, as one example, is an open source code). Reduced order modeling is another area that I see as a potentially useful in the near future but it would be challenging to train yourself in it without schooling.

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[IceBreakerSours]

While I was listening to something recently, I remembered watching an excellent set of linear algebra lectures by Gilbert Strang (YoTube MIT OCW). There is one set of lectures in which he talks about FEM and, with an extremely simple set of examples, he highlights the underlying ideas behind the connection between differential equations and linear algebra. Strang made fundamental mathematical contributions to FEM but he doesn't go into any detail so the course should be a breeze. Tip: Speed those videos up by 50%, if you decide to watch them.

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