What is exact reason behind choosing basic primitive shapes for elements in FEA?

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Discussion Overview

The discussion revolves around the reasons for choosing basic primitive shapes, such as triangles and tetrahedrons, for elements in finite element analysis (FEA). Participants explore the implications of these choices in both 2D and 3D contexts, questioning why more complex shapes like hexagons or pentagons are not standardized.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants suggest that all shapes can be decomposed into triangles, which may justify the preference for triangular elements.
  • There is a discussion about why only basic shapes are standardized, with some arguing that they are sufficient to describe any shape, especially with the use of midside nodes for arbitrary shapes and quadratic interpolation.
  • Participants mention that using complex shapes like dodecahedrons would not provide advantages over simpler elements due to the limitations of discrete nodes and the complexity of stiffness matrices.
  • A later reply questions the effectiveness of quads/hexahedrons compared to triangles/tetrahedrons, noting that fewer quads/hexahedrons may be needed for comparable analytical solutions.
  • Some participants express that quads are easier to control and can lead to smoother mesh lines, potentially avoiding erroneous results.
  • There is a mention of fundamental advantages between brick and pyramidal elements regarding solution accuracy and mesh quality, but uncertainty remains about the benefits of more complex elements.
  • Participants also discuss the relationship between element shapes and interpolation functions, questioning the lack of use for shapes like octagons and pentagons in 2D meshing.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the superiority of certain element shapes, and multiple competing views remain regarding the effectiveness and necessity of using basic primitive shapes versus more complex shapes in FEA.

Contextual Notes

Participants note that while some shapes can be broken down into triangles, the implications for stiffness matrices and solution accuracy are not fully resolved. The discussion highlights the complexity of choosing element shapes based on various factors, including mathematical considerations and practical applications.

Who May Find This Useful

This discussion may be useful for students and professionals interested in finite element analysis, particularly those exploring the theoretical and practical aspects of element shape selection in FEA.

mvpunekar
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what is exact reason behind choosing basic primitive shapes for elements in FEA?

Why it can't be hexagonal, pentagonal, octagonal, etc. in both cases 2D and 3D...

Thanks in advance...
 
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All of the shapes you've described can be decomposed into pyramids (triangles).
 
Mech_Engineer said:
All of the shapes you've described can be decomposed into pyramids (triangles).


Thanks for reply...

Its true...but why those small elements can take any other shape...

why only those basic shapes are standardised?
 
Mech_Engineer said:
All of the shapes you've described can be decomposed into pyramids (triangles).

how interpolation functions are affected by choosing higher primitive shapes??
 
mvpunekar said:
Thanks for reply...

Its true...but why those small elements can take any other shape...

why only those basic shapes are standardised?

They're the only ones neceaary to describe any shape under the sun, especially when you take into account midside nodes which allow arbitrary shapes and quadratic interpolation. take for example this ANSYS element:

gELEM152-1.gif


An element that was shaped like a dodecahedron would still be subject to the limitations of triangular elements, since it has faceted sides with discrete nodes; there is no advantage to using a huge element with a million faces when you can use a million elements with single faces.
 

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  • gELEM152-1.gif
    gELEM152-1.gif
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For some more examples:

Pyramid with midside nodes:
[PLAIN]http://www.me.cmu.edu/academics/courses/NSF_Edu_Proj/Statics_Solidworks/tutorial%20pictures/ansys/10%20node%20tet.gif

Brick with midside nodes:
[URL]http://research.me.udel.edu/~lwang/teaching/MEx81/ansyshelp/graphics/gELEM95-1.gif[/URL]
 
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Mech_Engineer said:
For some more examples:

Pyramid with midside nodes:
[PLAIN]http://www.me.cmu.edu/academics/courses/NSF_Edu_Proj/Statics_Solidworks/tutorial%20pictures/ansys/10%20node%20tet.gif

Brick with midside nodes:
[PLAIN]http://research.me.udel.edu/~lwang/teaching/MEx81/ansyshelp/graphics/gELEM95-1.gif[/QUOTE]

Thanks for such wonderful explanation...
 
Last edited by a moderator:
A follow-up question from me: Why does it seem like pretty much every mesher aims to create quads/hexahedrons, and from my own experience quads/hexahedrons blows away triangles/tetrahedrons in terms of density/precision of result; fewer quads/hexa are required to reach a comparable analytical solution.
 
Claws said:
A follow-up question from me: Why does it seem like pretty much every mesher aims to create quads/hexahedrons, and from my own experience quads/hexahedrons blows away triangles/tetrahedrons in terms of density/precision of result; fewer quads/hexa are required to reach a comparable analytical solution.

Thanks for help...

but can u relate ur answer to interpolation functions??

why elements like octagon, pentagon,etc are not used for 2D meshing(also in solids)?
 
  • #10
Claws said:
A follow-up question from me: Why does it seem like pretty much every mesher aims to create quads/hexahedrons, and from my own experience quads/hexahedrons blows away triangles/tetrahedrons in terms of density/precision of result; fewer quads/hexa are required to reach a comparable analytical solution.

Quads are typically easier to "control". The mesh lines are smooth, so I can typically avoid erroneous results from rapidly changing element shapes and sizes. In addition to that, you typically find that you can get a better mesh with much fewer elements using "brick" elements.
 
  • #11
mvpunekar said:
Thanks for help...

but can u relate ur answer to interpolation functions??

why elements like octagon, pentagon,etc are not used for 2D meshing(also in solids)?

As I explained, both an octagon and pentagon can be broken down into triangles; there is no advantage to use a larger element when it will have a much larger stiffness matrix to solve. There are fundamental advantages between brick and pyramidal elements in terms or solution accuracy and mesh quality, but I can't think of any reasons a more complex element would be better.
 
  • #12
Mech_Engineer said:
As I explained, both an octagon and pentagon can be broken down into triangles; there is no advantage to use a larger element when it will have a much larger stiffness matrix to solve. There are fundamental advantages between brick and pyramidal elements in terms or solution accuracy and mesh quality, but I can't think of any reasons a more complex element would be better.

now i got it perfectly ...thanks Mech engg...:smile: :smile:
 
  • #13
mvpunekar said:
now i got it perfectly ...thanks Mech engg...:smile: :smile:

Mech_Engineer said:
As I explained, both an octagon and pentagon can be broken down into triangles; there is no advantage to use a larger element when it will have a much larger stiffness matrix to solve. There are fundamental advantages between brick and pyramidal elements in terms or solution accuracy and mesh quality, but I can't think of any reasons a more complex element would be better.

can u provide some links to clear basics of FEm from practicality point of view...
 
  • #14
You can just do a search on Google. Some results that will come up are like this:

http://www.colorado.edu/engineering/cas/courses.d/IFEM.d/"
 
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  • #15
Mech_Engineer said:
You can just do a search on Google. Some results that will come up are like this:

http://www.colorado.edu/engineering/cas/courses.d/IFEM.d/"

Thanks again :smile:

by the way ,,,whats ur specialisation ??

n where r u from??
 
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  • #16
Mech_Engineer said:
You can just do a search on Google. Some results that will come up are like this:

http://www.colorado.edu/engineering/cas/courses.d/IFEM.d/"

This books has more mathematical approach ..

can u provide me links which teaches basic from pratical point of view ...like there is one book called "Practical Finite Element Analysis" by Nitin Gokhale, Finite to Infinite Publications...


Thanks in advance
 
Last edited by a moderator:
  • #17
mvpunekar said:
This books has more mathematical approach ..

can u provide me links which teaches basic from pratical point of view ...like there is one book called "Practical Finite Element Analysis" by Nitin Gokhale, Finite to Infinite Publications...

Thanks in advance

In case you didn't realize it let me clear something up for you- finite element analysis is ALL math. You can't learn about FEA without math, period. Even if you want a book with "pratical" in the name, it doesn't mean it won't cover the math aspects of FEA.

I'm a mechanical engineer, my job involves a lot of FEA analysis. Structural, thermal, electromagnetic, CFD, and coupled-physics.
 
  • #18
Mech_Engineer said:
In case you didn't realize it let me clear something up for you- finite element analysis is ALL math. You can't learn about FEA without math, period. Even if you want a book with "pratical" in the name, it doesn't mean it won't cover the math aspects of FEA.

I'm a mechanical engineer, my job involves a lot of FEA analysis. Structural, thermal, electromagnetic, CFD, and coupled-physics.

Thanks

But i have seen in some big companies that the Sr FEA engineers r just good at application part ...and not good in basics of maths of FEA... i guess only practical application of FEA is necessary & not its all core maths...its necessary for ppl who r developing those softwares?? isn't it?

anyways myself i have started learning FEA, ansys n Hypermesh ...will ask u whenever i get some doubts ...

Thankss in advance
 

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