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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

address practical advice about applying the method in practice [Budynas, 2011, Kim and Sankar,

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

Analysis Step Mistakes Made

Preliminary Analysis 1,2,3,7,9

Pre-processing 3,6,9,10

Solution 0

Post-processing 2,4,5

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