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69
C H A P T E R 5
Wisdom Is Doing It
In theory, theory and practice are the same. In practice,
they are not.
Albert Einstein
Do you know the diﬀerence between knowledge and
wisdom? Wisdom is doing it!
Dan Millman
A Peaceful Warrior
Sometimes it is said that the application of science or a theory is “as much an art as a science.”
e practice of the ﬁnite element method ﬁts the bill. Several authors have collected their own
practical tips for application of the method. But, in general, books primarily about ﬁnite element
theory do not present details regarding use of the method in practice. Books that attempt to
2009] almost always address issues that can be traced to the original list of ten most common
mistakes presented in Chapter 1. Consider that the method is comprised of the following.
1. Preliminary analysis, which may entail:
(a) simplifying the problem to obtain an analytical solution or estimation based on theory,
(b) obtaining theoretical solutions representing upper or lower bounds for the solution, or
(c) calculating the order of expected values for deﬂections and stresses and locations for
their respective maxima/minima.
2. Pre-processing, which usually includes:
(a) choosing an appropriate ﬁnite element formulation,
(b) discretizing the domain globally,
(c) reﬁning it locally in areas of interest, and
(d) applying loads and displacement constraints.
70 5. WISDOM IS DOING IT
3. Solving the equations.
4. Post-processing the solution variables to compute
(a) reaction forces and
(b) internal stresses.
5. Interpreting and validating numerical solution results.
Referring to the list of most commonly made mistakes reported in Chapter 1, we attempt
to correlate this list with the steps performed in the ﬁnite element method in Table 5.1. Five of
the ten common errors might be avoided by paying particular attention to a well-performed pre-
liminary analysis. Errors in pre-processing result in four of the typical errors. ere is substantial
overlap as preliminary analysis directly aﬀects the most substantial step in pre-processing, which
is discretizing the domain. Finally, three commonly made mistakes can be avoided with prudent
post-processing. e solution of the equations for nodal point equilibrium usually results in no
errors.
Note To e Instructor
While it is always important for students to know what a piece of computational software is doing on
their behalf, having students mathematically carry out the steps of computing element equations, assembling
them into a global matrix equation, reducing its rank once the boundary conditions have been decided, and
solving the reduced set of equations will all be done for them in practice by commercial software. Because
of the relative importance of the other mistakes they will likely make, we question the utility of assigning
students problems requiring this mathematics. Many times, these are precisely the types of assignments that
are given in an introductory course in the ﬁnite element method. It may behoove all of us who teach the
method to realize that if we only have a single chance to speak to students on behalf of the method, we
should at least discuss the list of places they will likely make mistakes. We also might be of better service to
their education by assigning open-ended problems that require them to focus more on the steps where they
are most likely to err while we are available to intervene and correct any ongoing misconceptions and poor
practices before they become matters of routine.
Table 5.1: Mistakes listed by Chalice Engineering, LLC [2009] fall solely within portions of the
analysis process performed by the analyst