Math vs. FE Method: Comparing Mechanical Engineering Focus

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In summary: The FE METHOD was developed by engineers (civil: trusses, frames, etc.; and mechanical: solids, plane stress, etc.) As such, it is a METHOD of applying the ALGORITHM in pre-set ways for mechanical engineering: to read in connectivity, set up Jacobians, set up Gauss Q. integration, set up the B matrix, B-transpose * B * B, etc. I don't think the math departments teach this properly for mechanical engineers. I have seen students take FE classes from math departments and come out without any idea that there really is an established approach to a METHOD.In summary, the math courses offered by a
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How would you describe the FE method
I have written FE codes.
I have seen FE classes from mechanical engineering
I have seen FE classes from the math departments

When offered from a math department, the focus is the theory (with a lot of attention paid to general differential equations)
They are good courses and they suggest, I think AN ALGORITHM

However in the Finite Element Method, to ME the operative word is METHOD

And I am hoping someone can say what I am about to say, more precisely:

The FE METHOD was developed by engineers (civil: trusses, frames, etc.; and mechanical: solids, plane stress, etc.) As such, it is a METHOD of applying the ALGORITHM in pre-set ways for mechanical engineering: to read in connectivity, set up Jacobians, set up Gauss Q. integration, set up the B matrix, B-transpose * B * B, etc. I don't think the math departments teach this properly for mechanical engineers. I have seen students take FE classes from math departments and come out without any idea that there really is an established approach to a METHOD.

Can someone help me say this better? (Or, maybe I am wrong?) I am not sure I have the right to abuse the word METHOD and ALGORITHM as I do.
 
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Is it fair to say that the math course still leaves you with some decisions to make based on your specific application, whereas the ME course is already specialized to a particular application?

It would also not surprise me if the math course goes into more detail about how and why the method works.
 
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Trying2Learn said:
I don't think the math departments teach this properly for mechanical engineers. I have seen students take FE classes from math departments and come out without any idea that there really is an established approach to a METHOD.
Well, when I was studying at the mechanical faculty, the FEM course was strictly about the math behind this method - vector spaces, weak forms, Galerkin method and basis/shape functions. Not a single word about applications of this mathematical method in mechanics. Now they teach the opposite - pure practice (how to use a particular FEA software). Neither of these approaches is good and the first one is literally terrible for mechanical engineers. It should be theory (not math but its application in mechanical problems) plus some practice. Like many other FEA engineers, I had to spend a lot of time on self-learning. Fortunately, apart from usually very academically focused books about FEA, there are also several blogs with a good introduction to FEM theory and after understanding the basics one may proceed to more advanced content included in classic books (I wouldn't recommend the trilogy by Zienkiewicz though).

I think that in order to understand how FEA software actually works, it's best to take a closer look at examples involving hand calculations of simple structures. Starting from springs, proceeding to bars/beams and finally flat plates. The latter are particularly important, among others, because they show how the stiffness matrix is obtained when the direct approach cannot be used and thus how it's actually implemented in FEA codes.
 
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FAQ: Math vs. FE Method: Comparing Mechanical Engineering Focus

1. What is the difference between math and the FE method in mechanical engineering?

Math and the Finite Element (FE) method are both used in mechanical engineering to solve complex problems and analyze systems. However, the main difference between the two is that math is a theoretical approach while the FE method is a numerical approach. Math involves using equations and formulas to solve problems analytically, while the FE method uses a computer-based approach to divide a complex system into smaller, simpler parts for analysis.

2. Which method is more accurate, math or the FE method?

Both math and the FE method can provide accurate results when used correctly. However, the accuracy of the results can depend on the complexity of the problem and the assumptions made in the analysis. In general, the FE method is considered to be more accurate for complex systems with irregular geometries, while math may be more accurate for simpler systems with regular geometries.

3. How does the FE method save time compared to using math in mechanical engineering?

The FE method can save time in mechanical engineering by automating the process of solving complex problems. In math, each problem must be solved analytically, which can be time-consuming, especially for complex systems. With the FE method, the computer does the calculations and analysis, allowing for faster and more efficient problem-solving.

4. Is one method preferred over the other in mechanical engineering?

There is no one preferred method in mechanical engineering, as both math and the FE method have their own advantages and disadvantages. The choice of method often depends on the specific problem and the resources available. In some cases, a combination of both methods may be used to achieve the most accurate and efficient results.

5. Can the FE method completely replace the use of math in mechanical engineering?

No, the FE method cannot completely replace the use of math in mechanical engineering. While the FE method is useful for solving complex problems, it still relies on mathematical principles and equations for its calculations. Additionally, math is still necessary for theoretical analysis and for verifying the results obtained from the FE method.

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