ADVANCED MECHANICS OF MATERIALS AND APPLIED ELASTICITY PDF
This text is an outgrowth of the material used by the author for several decades in senior
and graduate courses for students of mechanical, aerospace and civil engineering. It deals
with the problem of computing the stress and displacement fields in solid bodies at two
levels of approximation: the level of the linear theory of elasticity and the level of the
theories of mechanics of materials. The linear theory of elasticity is based on very few
assumptions and can be applied to bodies of any geometry.
The theories of mechanics of
materials are based on many assumptions in addition to those of the theory of elasticity and
they can be applied only to bodies of certain geometries (beams, bars, shafts, frames, plates
shells and thin-walled, tubular members). In this text the formulas of the theories of
mechanics of materials are derived in a way that the assumptions on which they are based
can be clearly understood. Moreover, wherever possible the results obtained on the basis of
the theories of mechanics of materials are compared with those obtained on the basis of the
theory of elasticity.
In the past, the use of the linear theory of elasticity was limited by the fact that only a few
problems could be solved using the available classical methods. Thus, approximate theories
like the theories of mechanics of materials were formulated for which exact solutions could
be found. With the advent of the electronic computer, many problems involving bodies
whose geometry does not justify the use of the theories of mechanics of materials, are
formulated on the basis of the linear theory of elasticity and solved approximately with the
aid of a computer.
Thus, a mechanical, civil or aerospace engineer who works in the area of
stress analysis and design often uses software based on the linear theory of elasticity. It is
important therefore that master’s level students of mechanical, aerospace and civil
engineering who specialize in the area of stress analysis and design, should acquire some
knowledge of applied elasticity.
The book includes 18 chapters and 7 appendices. In the first chapter a brief review of
vector analysis is presented followed by a very elementary, but concise introduction to the
algebra of symmetric tensors of the second rank. In the theories of mechanics of materials
and elasticity one deals with quantities such as stress, strain and moments and product of
inertia which are symmetric tensors of the second rank. It is desirable therefore that the
student learns at the very beginning the transformation properties of such quantities as well
as how to determine their stationary values.
The boundary value problems for computing the displacement and stress fields in solid
bodies on the basis of the linear theory of elasticity, are formulated in Chapter 5 and applied
to simple examples in Chapters 5, 6 (torsion problem) and 7 (plain stress and plain strain
problems). The boundary value problems for computing the displacement and stress fields
on the basis of the theory of mechanics of materials are presented in Chapters 8 and 9 for
bodies made of prismatic line members, in Chapter 10 for nonprismatic line members, in
Chapter 11 for curved line members, in Chapter 12 for tubular members and in Chapters 17
for plates. Part of the material presented in Chapters 8 and 9 is available in elementary texts
of strength of materials. It is included in this text for completeness of our presentation and
for those who need a review of this material at a slightly more advanced level than that of
the elementary texts.