xii PREFACE
In laying this path, we deliberately employ an approach to emphasize and exploit the natural
ties between classical Mechanics of Materials (MoM) and FEA, and which is motivated, in part,
by the philosophy articulated in Papadopoulos et al. [2011]. Of course, equally deep ties exist
between elasticity theory and FEA, but as our focus is developing expertise of undergraduates,
we appeal primarily to the ties between FEA and MoM.
In this approach, we provide examples in which FEA can be used to confirm results of
hand calculation, closed form solutions, or standard tables—and vice versa—helping students to
build confidence in all. e book then explores more advanced user habits such as formulating
expectations, making estimates, and performing benchmark calculations. Broadly speaking, this
book responds to the growing call to include simulation as a basic engineering competency, and
will help to promote the development of a culture of using simulation in the undergraduate en-
gineering curriculum.
As such, we envision this book being used as a companion to a traditional textbook in an
upper-level undergraduate FEA course and also as an instructional guide for practice in other
courses in which FEA is applied, including courses as early as freshman design and introductory
mechanics. Even at these early stages, instructors can judiciously draw from the book to plant
the seeds of good habits in their students. is book is written in language that is immediately
transparent to instructors and accessible to students who have completed a basic course in MoM.
Terminologies that might be advanced to the novice user are italicized and explained in the context
of their use.
PEDAGOGICAL APPROACH
e pedagogical strategy of this book is based in the educational theory of constructivism and
related research in misconceptions. e essence of constructivist philosophy to which we appeal
here is rooted in the work of cognitive psychologist Jerome Bruner, and is succinctly described
by Montfort et al. [2009]: “learning [is] a complex process in which learners are constantly read-
justing their existing knowledge and, more importantly, the relationships between the things that
they know.” Further, this readjustment process requires that the learner not just passively receive
information, but actively enter into the “discovery of regularities of previously unrecognized re-
lations and similarities between ideas, with a resulting sense of self-confidence in one’s abilities”
[Bruner, 1960].
One way to involve students in the processes of readjusting and discovering knowledge
is by anticipating their misconceptions and providing exercises and activities that force them to
reevaluate their original assumptions and conceptions. For at least three decades, science and
engineering educators have realized the importance of identifying and addressing misconceptions,
suggesting that educators should directly address misconceptions by some combination of early
intervention and an infusion of activities that force students to face the misconceptions head-
on [Hake, 1998, McDermott, 1984, Montfort et al., 2009, Papadopoulos, 2008, Streveler et al.,
2008]. Broadly speaking, “active learning,” “problem based learning,” “inquiry based learning,”
PREFACE xiii
and “student centered learning” approaches aim to accomplish this. Ken Bain, in his book, What
the Best College Teachers Do, champions this view:
Some of the best teachers want to create an expectation failure, a situation in which
existing mental models lead to faulty expectations. ey attempt to place students in
situations where their mental models will not work. ey listen to student concep-
tions before challenging them. ey introduced problems, often case studies of what
could go wrong, and engaged the students in grappling with the issues those examples
raised [Bain, 2004].
Physics educator Lillian McDermott further adds that “students need to participate in the process
of constructing qualitative models and applying these models to predict and explain real-world
phenomena” [McDermott, 2001].
It is important to observe that this type of instruction requires a high degree of interaction
and feedback on the part of the teacher and a correspondingly high degree of self-inquiry on the
part of the learner. In this environment, teachers need to allow students to test ideas, and lend
support in tweaking those ideas into a more correct model of how things happen, and students
must eagerly participate in this process of discovery.
In the spirit of those instructors who have successfully accomplished this, we seek to provide
students with the support they need to cognitively rewire. Indeed, many of the examples and
exercises are deliberately designed to confront readers with expectation failures and to provide
them ample opportunity to develop models that appropriately match reality, but which also require
instructors to intervene as supportive mentors. With this approach, novices and students will
develop the good habits required of experienced users.
In the particular case of FEA, many of the common pitfalls repeatedly encountered by an-
alysts are rooted in a mixture of inadequacies in their understanding of MoM theory, modeling,
and the useful approximations particular to FEA, as well as their inability to integrate these areas
of knowledge. To address these matters, we aim to strike a prudent balance between theory and
practical application. We suggest that this is best accomplished by prescribing a minimal requisite
skill set, rooted in mastery of MoM, upon which the modeling decisions required in the finite el-
ement method are based. is mastery of the most rudimentary underlying theory helps students
make fewer of the errors in judgement when validating their numerical simulations.
Ultimately, our emphasis is to provide an instructional approach that is amenable to a prac-
ticing engineer rather than a mathematician. We attempt to cultivate the habit of care that is
necessary to perform good quality engineering analysis. When answering the question “What is
a university for?,” New York Times columnist David Brooks wrote:
[to obtain] technical knowledge and practical knowledge. Technical knowledge is for-
mulas…that can be captured in lectures. Practical knowledge is not about what you
do, but how you do it. It can not be taught or memorized, only imparted and absorbed.
It is not reducible to rules; it only exists in practice [Brooks, 2013].
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