3.3. UTILITY OF THE FINITE ELEMENT METHOD 45
3.3 UTILITY OF THE FINITE ELEMENT METHOD
e deviations from the simplest stress states that occur in the examples of Sections 3.1 and 3.2
are easily handled by the finite element method. Deviations such as stress concentrations may
be predicted using approximate formulae, but these are almost always dependent on details of
the specimen geometry; FEA, in contrast, is simple enough to apply in all of these cases and
does a good job predicting the correct behavior for elastic deformation and stress. As the finite
element method becomes more pervasively used in industry, we feel there is utility in introducing
the method earlier in engineering curricula [Papadopoulos et al., 2011]. Distinct advantages to
introducing the method throughout one’s undergraduate studies include reducing the drudgery
and potential errors of computation, focusing on the theory of mechanics, while enabling students
to approach more complicated problems that escape the realm of closed-form solutions.
Now recall our earlier point that when using pre-programmed software, the majority of the
errors and their severity are attributable to the user. ese include faulty input, poor modeling,
poor pre-processing, and ignorance of the software protocol. Analogous errors of using a wrong
formula or remaining ignorant of a key formula can occur when using hand calculations [Jeremić,
2009, Papadopoulos et al., 2011, Prantil and Howard, 2007, 2008]. e potential for such error
in problems like the ones in this chapter is high because the theoretical solutions are likely beyond
what most undergraduate mechanical engineering students have learned.
Here FEA can be very beneficial to allow students to explore behavior beyond their basic
theoretical knowledge, and it can serve as a bridge for them to discover more advanced theoretical
treatments that appear, such as Gieck and Gieck [2006] and Young and Budynas [2002]. Such
books are good references for finite element analysts to have at hand for validating numerical
solutions for problems whose analytical or empirical solutions have been determined. Using these
solutions as benchmarks for FEA analyses helps reinforce the practice of finding published and
verified solutions for comparison with numerical simulations. is further underscores our earlier
point that we advocate early introduction of FEA in the curriculum, even when it appears to
precede the students’ current level of engineering knowledge [Papadopoulos et al., 2011].
While applying the finite element method in these cases is relatively straightforward, for
more complex geometries and boundary conditions, the prescription of model details leads to sit-
uations in which it can become progressively easier for analysts to go wrong applying the method.
We discuss illustrative case studies for two such boundary value problems in Chapter 4.
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