12 2. LET’S GET STARTED
of what we regard are the minimum essential elements of MoM theory required to undertake
study of FEA. We close with two examples that can be solved by hand calculation as a means to
illustrate the finite element method.
Some colleagues are concerned that use of FEA in early courses might supplant a strong
understanding of Mechanics of Materials principles because the effort normally done by hand
can now be done by “pressing a few buttons.” We insist that this is neither our point of view nor a
circumstance that is likely to occur under a pedagogy that is committed to ensuring that students
form good habits of understanding modeling assumptions and validation procedures. We insist
that use of FEA requires even more theoretical understanding so that it can be applied with skill.
e usual adjuration to “calculate problems first by hand” can then be re-interpreted as “take steps
to validate and benchmark your FEA solution.”
2.1 QUALITATIVE CONCEPTS OF MECHANICS OF
MATERIALS
Here we present a list of qualitative concepts that can be read at once by novices and experts,
motivated by ideas presented in [Papadopoulos et al., 2011]. While the expert will recognize
many of these ideas from experience, the novice can begin to appreciate the qualitative concepts
and ideas that a more seasoned practitioner uses with confidence and fluency. We recommend
that students periodically return to this list after doing some of the example problems so that they
can develop a better feel for how these ideas appear in practice. e presence of this list at the
beginning of the chapter should not be interpreted to mean that the student must master this list
all at once on first reading. Rather, practice itself is what will help the student to internalize these
ideas and develop the fluency of an expert. is list of qualitative concepts is as follows.
• All structures, no matter how strong, are deformable at least to a small degree. is means
that when loads are applied, the material points in the structure move or displace. Many
structural elements can be modeled as simple springs as a means to understand the relation-
ship of force to displacement in the structure.
• Studying the exact geometry of a structure and its actual displacements under loading can
be very complicated with many resulting equations being nonlinear. In many structures of
practical interest, however, the displacements will remain small compared to the overall size
of the structure, and simple small displacement approximations can be made that lead to
simpler, linear relations. Such linearity renders the ability to superpose basic solutions, or
to scale any solution in load or overall size.
• One has the ability to interpret a result in terms of basic ideas or elementary asymptotic
solutions. For example, the bending moment transmitted by a cross section; the force and
moment equilibrium of loads plus reactions; the maximum bending or twisting strain at an
outer fiber; and rigid body degrees of freedom of a body or system.
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