1.4. MAN VS. MACHINE 5
While it may come as no surprise, novice users commit many, if not all, of these errors.
But these errors continue to be committed routinely even by advanced users and engineers in
industrial practice. As suggested earlier, we attribute this to a lack of a minimal requisite skill
set (or an inability to apply such fluently). is lack of understanding is due, at least in part, to
computational complacency [Paulino, 2000] and the optimism bias [Conly, 2013] cited earlier.
Avoiding such errors is not simply a matter of telling and re-telling the student “how to do
it.” Most students learn by repeated attempts in the face of incorrect reasoning and results. It is
through repeated corrections in the face of practice that we learn, not simply by being presented
with how things ought to work. erefore, before a sense of good modeling practice can truly be
learned and internalized, the student must come to appreciate the value of being skeptical about
initial numerical simulations, i. e., that they are guilty until proven innocent. Students must realize
and care that their intuition might be incorrect. en they must actively work to deconstruct their
previously incorrect model, and replace it with a model with deeper understanding. Likewise,
the good instructor must provide a supportive environment in which students are encouraged to
explore problems in which they are likely to make errors, and then coach them to be self-critical,
to realize and understand the errors that they have made.
Indeed, as suggested by the attention on student misconceptions in the literature on peda-
gogy [Hake, 1998, McDermott, 1984, Montfort et al., 2009, Papadopoulos, 2008, Streveler et al.,
2008], when students are forced to work out a problem with judicious questioning and investiga-
tion where their initial reasoning was incorrect—again, in Ken Bain’s words, an expectation failure
[Bain, 2004]—their learning retention is greater, and their recall and critical thinking skills are
enhanced. We take up this point further in the last section of this chapter when we recommend
our pedagogical strategy for FEA.
1.4 MAN VS. MACHINE
It’s foolish to swap the amazing machine in your skull
for the crude machine on your desk. Sometimes, man
beats the machine.
David Brooks
e New York Times
It is noteworthy that many introductory texts for the study of finite element analysis make use of
some form or the other of the necessary procedural steps in applying the method in practice. en
students are provided exercises in applying these procedural steps by means of hand calculations.
e procedural steps that a typical finite element analysis should include are as follows:
Ask what the solution should look like: An analyst must have some idea of what to expect in
the solution, e. g., a stress concentration, and other characteristics of the solution, such as
symmetry.
6 1. GUILTY UNTIL PROVEN INNOCENT
Choose an appropriate element formulation: One needs to understand, from knowledge of the
expected solution, what elemental degrees of freedom and polynomial order of approxima-
tion are necessary to accurately model the problem.
Mesh the global domain: With knowledge of the expected solution and the chosen order of in-
terpolation—the estimation of the solution at a general location based on the computed
solution at the grid points of the mesh (the order of which could be linear, quadratic, etc.),
one can wisely select a number and arrangement of elements necessary to adequately capture
the response.
Define the strain-displacement and stress-strain relations: It is important to know what for-
mulation your commercial software code has programmed into the analysis module. Clas-
sical small strain relations are appropriate for linear, static stress analysis. e user must
provide a constitutive law relating stress and strain.
Compile the load-displacement relations: e element matrix equations are either derived in
closed form a priori or computed via numerical integration within the analysis code.
Assemble the element equations into a global matrix equation: is step is performed algo-
rithmically with knowledge of the element degrees of freedom and nodal connectivity. is
global equation relates externally applied conjugate forces and associated nodal point de-
grees of freedom. It represents a generalized form of nodal point equilibrium.
Apply loads and boundary conditions: Because there are multiple prescriptions of statically
equivalent loads and boundary constraints, their precise prescription must be justified based
on problem symmetry and proximity to internal regions where accurate stress results are
most desired.
Solve for the primary nodal degrees of freedom: Solve the appropriately reduced global matrix
equation.
Solve for the derivatives of primary degrees of freedom: is involves calculating generalized
reaction forces at nodes and strains and stresses within elements.
Interpret, verify, and validate the results: Based on comparisons with initial expectations, ex-
perimental data, analytical benchmark results, or other reputable numerical solutions, have
the calculated results converged and are they reasonable?
Again, the novice might not completely understand or appreciate the meaning of each
step at this time. However, he or she can still gain some sense and insight into the procedure.
In particular, it is very telling that the steps break down succinctly into those performed by the
analyst and those performed by the computer. Even the novice will appreciate the complementary
roles of the human and the machine from the very outset.
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