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Eighty Years of the Finite Element Method (2022)

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Re: Eighty Years of the Finite Element Method (2022)

#81

Post by physicsguy »

magicalhippo wrote: post #30
lll-o-lll wrote: post #19

Earlier quoted context omitted.

Interesting. Please bear with me as this is going off 25 year old memories, but my memory is that the workflow for using FEA tools was: Model in some 3D modelling engineering tool (e.g. SolidWorks), ansys to run FEA, iterate if needed, prototype, iterate. So to have anything useful, you need that entire pipeline? For hobbyists, I assume we need this stack. What are the popular modelling tools?

Yeah not my domain so wouldn't really know. For FEniCS I know Gmsh[1] was used. There's some work[2][3] been done to integrate FEniCS with FreeCAD. It seems FreeCAD also supports[4] other FEM solvers. But, I guess you get what you pay for in this space still. [1]: https://gmsh.info/ [2]: https://github.com/qingfengxia/Cfd [3]: https://github.com/qingfengxia/FenicsSolver [3]: https://wiki.freecad.org/FEM_Solver

You can export other CAD meshes for use in it

Re: Eighty Years of the Finite Element Method (2022)

#82

Post by drpossum »

sashank_1509 wrote: post #40
antegamisou wrote: post #22

Earlier quoted context omitted.

Good luck designing crash resilient structures without simulating it on FEM based software though.

I’d guess most of the bridges in US were built before FEM existed

The average age of a bridge in the US is about 40-50 years old and the title of the article has "80 years of FEM".

https://www.infrastructurereportcard.org/wp-content/uploads/...

I'd posit a large fraction were designed with FEM.

Re: Eighty Years of the Finite Element Method (2022)

#83

Post by physicsguy »

lll-o-lll wrote: post #19
magicalhippo wrote: post #6

Earlier quoted context omitted.

> Still no viable open-source solution. For the more low-level stuff there's the FEniCS project[1], for solving PDEs using fairly straight forward Python code like this[2]. When I say fairly straight forward, I mean it follows the math pretty closely, it's not exactly high-school level stuff. [1]: https://fenicsproject.org/ [2]: https://jsdokken.com/dolfinx-tutorial/chapter2/linearelastic...

Interesting. Please bear with me as this is going off 25 year old memories, but my memory is that the workflow for using FEA tools was: Model in some 3D modelling engineering tool (e.g. SolidWorks), ansys to run FEA, iterate if needed, prototype, iterate. So to have anything useful, you need that entire pipeline? For hobbyists, I assume we need this stack. What are the popular modelling tools?

FEniCs is mostly used by academic researchers, I used it for FEM modelling in magnetic for e.g. where the sorts of problems we wanted to solve you can’t do in a commercial package.

Re: Eighty Years of the Finite Element Method (2022)

#84

Post by karencarits »

weinzierl wrote: post #3

I started my career doing FE modeling and analysis with ANSYS and NASTRAN. Sometimes I miss these days. Thinking about how to simplify a real world problem so far that it is solvable with the computational means available was always fun. Then pushing quads around for hours until the mesh was good had an almost meditative effect. But I don't feel overwhelmingly eager to learn a new software or language. Much to my sur…

OpenFOAM seems like an opensource option but I have found it rather impenetrable - there are some youtube videos and pdf tutorials, but they are quite dense and specific and doens't seem to cover the entire pipeline

Happy to hear if people have good resources!

Re: Eighty Years of the Finite Element Method (2022)

#85

Post by drpossum »

tightbookkeeper wrote: post #37
antegamisou wrote: post #22

Earlier quoted context omitted.

Good luck designing crash resilient structures without simulating it on FEM based software though.

They did this just fine until without such tools for the majority of innovation in the last century.

Having worked on the design of safety structures with mechanical engineers for a few projects, it is far, far cheaper to do a simulation and iterate over designs and situations than do that in a lab or work it out by hand. The type of stuff you can do on paper without FEM tends to be significantly oversimplified.

It doesn't replace things like actual tests, but it makes designing and understanding testing more efficient and more effective. It is also much easier to convince reviewers you've done your job correctly with them.

I'd argue computer simulation has been an important component a majority of mechanical engineering innovation in the last century. If you asked a mechanical engineer to ignore those tools in their job they'd (rightly) throw a fit. We did "just fine" without cars for the majority of humanity, but motorized vehicles significantly changed how we do things and changed the reach of what we can do.

Re: Eighty Years of the Finite Element Method (2022)

#86

Post by formerly_proven »

somat wrote: post #45
antegamisou wrote: post #22

Earlier quoted context omitted.

Good luck designing crash resilient structures without simulating it on FEM based software though.

The FEM is just a model of the crash resistant structure. Hopefully it will behave like the actual structure, but that is not guaranteed. We use the FEM because it is faster and cheaper than doing the tests on the actual thing. However if you have the time and money to do your crash resiliency tests on the actual product during the development phase. I expect the results would be much better.

Yes, with infinite time and budget you'd get much better results. That does not sound like an interesting proposition, though.

Re: Eighty Years of the Finite Element Method (2022)

#87

Post by meindnoch »

KeplerBoy wrote: post #77
meindnoch wrote: post #75

Earlier quoted context omitted.

But that's not true, unless by "average" you mean the median.

Normally, it's all the same.

Only if the distribution has zero skewness.

Unless "normally" you mean the normal distribution, which indeed has zero skewness.

Re: Eighty Years of the Finite Element Method (2022)

#88

Post by tightbookkeeper »

drpossum wrote: post #85
tightbookkeeper wrote: post #37

Earlier quoted context omitted.

They did this just fine until without such tools for the majority of innovation in the last century.

Having worked on the design of safety structures with mechanical engineers for a few projects, it is far, far cheaper to do a simulation and iterate over designs and situations than do that in a lab or work it out by hand. The type of stuff you can do on paper without FEM tends to be significantly oversimplified. It doesn't replace things like actual tests, but it makes designing and understanding testing more effici…

> It is also much easier to convince reviewers you've done your job correctly with them.

In other words, the work that doesn't change the underlying reality of the product?

> We did "just fine" without cars for the majority of humanity

We went to the moon, invented aircraft, bridges, skyscrapers, etc, all without FEM. So that's why this is a bad comparison.

> If you asked a mechanical engineer to ignore those tools in their job they'd (rightly) throw a fit.

Of course. That's what they are accustomed to. 80/20 paper techniques that were replaced by SW were forgotten.

When tests are cheap, you make a lot of them. When they are expensive, you do a few and maximize the information you learn from them.

I'm not arguing FEM doesn't provide net benefit to the industry.

Re: Eighty Years of the Finite Element Method (2022)

#89

Post by bgoated01 »

chipdart wrote: post #67
bgoated01 wrote: post #64

Interesting perspective. I just attended an academic conference on isogeometric analysis (IGA), which is briefly mentioned in this article. Tom Hughes, who is mentioned several times, is now the de facto leader of the IGA research community. IGA has a lot of potential to solve many of the pain points of FEM. It has better convergence rates in general, allows for better timesteps in explicit solvers, has better method…

> IGA has a lot of potential to solve many of the pain points of FEM. Isn't IGA's shtick just replacing classical shape functions with the splines used to specify the geometry? If I recall correctly convergence rates are exactly the same, but the whole approach fails to realize that, other than boundaries, geometry and the fields of quantities of interest do not have the same spatial distributions. IGA has been aroun…

> Isn't IGA's shtick just replacing classical shape functions with the splines used to specify the geometry?

That's how it started, yes. The splines used to specify the geometry are trimmed surfaces, and IGA has expanded from there to the use of splines generally as the shape functions, as well as trimming of volumes, etc. This use of smooth splines as shape functions improves the accuracy per degree of freedom.

> If I recall correctly convergence rates are exactly the same

Okay, looks like I remembered wrong here. What we do definitely see is that in IGA you get the convergence rates of higher degrees without drastically increasing your degree of freedom, meaning that there is better accuracy per degree of freedom for any degree above 1. See for example Figures 16 and 18 in this paper: https://www.researchgate.net/profile/Laurens-Coox/publicatio...

> geometry and the fields of quantities of interest do not have the same spatial distributions.

Using the same shape functions doesn't automatically mean that they will have the same spatial distributions. In fact, with hierarchical refinement in splines you can refine the geometry and any single field of interest separately.

> What is left in terms of potential?

The biggest potential other than higher accuracy per degree of freedom is perhaps trimming. In FEM, trimming your shape functions makes the solution unusable. In IGA, you can immerse your model in a "brick" of smooth spline shape functions, trim off the region outside, and run the simulation while still getting optimal convergence properties. This effectively means little to no meshing required. For a company that is readying this for use in industry, take a look at https://coreform.com/ (disclosure, I used to be a software developer there).

Re: Eighty Years of the Finite Element Method (2022)

#90

Post by goodtruck »

weinzierl wrote: post #3

I started my career doing FE modeling and analysis with ANSYS and NASTRAN. Sometimes I miss these days. Thinking about how to simplify a real world problem so far that it is solvable with the computational means available was always fun. Then pushing quads around for hours until the mesh was good had an almost meditative effect. But I don't feel overwhelmingly eager to learn a new software or language. Much to my sur…

I am hoping this open source FEM library will catch on : https://www.dealii.org/. The deal in deal.II stands for Differential Equation Analysis Library.

It's written in C++, makes heavy use of templates and been in development since 2000. It's not meant for solid mechanics or fluid mechanics specifically, but for FEM solutions of general PDEs.

The documentation is vast, the examples are numerous and the library interfaces with other libraries like Petsc, Trilinos etc. You can output results to a variety of formats.

I believe support for triangle and tetrahedral elements has been added only recently. In spite of this, one quirk of the library is that meshes are called "triangulations".

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