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Finite element method course?

  1. Oct 29, 2013 #1
    I am thinking about taking a finite element method course. I know what FEM is and how it solves boundary value problems and stuff but I'm wondering how widespread it is used...

    Is it a useful numerical technique? What industries/research use it? I am interested in research in continuum mechanics and engineering in general, should I take this course? Is it a narrow subject?
     
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  3. Oct 29, 2013 #2

    AlephZero

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    It is used very widely. Most CAD systems now have an "easy to use" FEM package built in. There are industry standard general-purpose FE programs like NASTRAN, ANSYS, ABAQUS, etc. There are more specialist programs for particular applications, e.g. crash simulations. And there is plenty of research to be done in "multi-physics" simulations (e.g. modeling a combustion process by combining heat transfer, fluid dynamics, chemistry, structural analysis, and anything else that seems relevant....)

    If your existing knowledge of FE is "math based" (I'm guessing that from your comment about "solving boundary value problems"), try to find some courses that emphasize the "practical" applications (e.g. real-world models of material behavior, the formulation of shell elements, the many aspects of nonlinear problems, etc).

    The subject is as wide or narrow as you want to make it. There is plenty of research to do - AFAIK MSC, the company that markets NASTRAN, has about 300 PhD-level employees working on software development. There is plenty of specialist research and software development in high-tech engineering companies as well - some of it very specialized to solving particular problems.
     
  4. Oct 29, 2013 #3
    Thanks, that was extremely informative. Does research in "multi-physics", multi-scale modeling, etc.. typically incorporate FEM? Is it the only technique or the most widely used technique for such simulations?
     
  5. Oct 30, 2013 #4
    Yes it does. It's not the only technique but I'd say it is the most widely used due to its generality. Finite volume or boundary element methods are also very common, but I'd say they aren't quite as general as the FEM, which makes it harder to incorporate a range of different governing equations within a single model.
     
  6. Oct 30, 2013 #5

    AlephZero

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    Finite element and finite volume methods are the same basic idea, if you don't restrict yourself to the original historical idea of the FE method, i.e. doing interpolation using "shape functions" defined by values at the element's nodes (grid points).

    Fluid dynamics has had a relatively long "love affair" with finite difference methods, but the problem of mesh generation for arbitrary geometries is ending that relationship, as CFD has moved to being a standard engineering tool with commercial software packages available, rather than a very expensive "research" activity.

    In structural analysis, I think boundary elements were something that "seemed like a good idea at the time", for efficient solution of some types of 2D problems with the limited computer power available in say the 1980s, but it doesn't scale well to large models (e.g. > 100,000 degrees of freedom) and nonlinear behavior, and in time-dependent problems there can be numerical conditioning problems trying the represent the response of the "internal" parts of the system purely in terms of the boundary. (That issue is inherent in the physics, not just an artifact of the numerical method). Some people have used "boundary element methods plus additional internal points" to get around that problem - but why bother to invent a new type of wheel, when you can use FEM or FVM instead?

    (BEM may be better suited to inherently linear problems such as electromagnetism - not my specialist subject, though)
     
  7. Oct 30, 2013 #6

    Astronuc

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    FEM is used in many engineering disciplines (civil, mechanical, aerospace, nuclear, . . . ), as well as physics (computational physics).

    I can be applied to mechanics/dynamics of solids and fluids (liquids and gases), and plasmas.

    http://numerik.iwr.uni-heidelberg.de/Oberwolfach-Seminar/CFD-Course.pdf

    These days, one will see a lot more in the realm of computational multiphysics.
     
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