GENERAL CONSIDERATIONS
The subject of Elasticity is concerned with the determination of the stresses and
displacements in a body as a result of applied mechanical or thermal loads, for those
cases in which the body reverts to its original state on the removal of the loads.
In this book, we shall further restrict attention to the case of linear infinitesimal
elasticity, in which the stresses and displacements are linearly proportional to the
applied loads and the displacements are small in comparison with the characteristic
length dimensions of the body. These restrictions ensure that linear superposition
can be used and enable us to employ a wide range of series and transform techniques
which are not available for non-linear problems.
Most engineers first encounter problems of this kind in the context of the subject
known as Mechanics of Materials, which is an important constituent of most undergraduate
engineering curricula. Mechanics of Materials differs from Elasticity in that
various plausible but unsubstantiated assumptions are made about the deformation
process in the course of the analysis. A typical example is the assumption that plane
sections remain plane in the bending of a slender beam. Elasticity makes no such
assumptions, but attempts to develop the solution directly and rigorously from its
first principles, which are Newton’s laws of motion, Euclidian geometry and Hooke’s
law. Approximations are often introduced towards the end of the solution, but these
are mathematical approximations used to obtain solutions of the governing equations
rather than physical approximations that impose artificial and strictly unjustifiable
constraints on the permissible deformation field.
However, it would be a mistake to draw too firm a distinction between the two
approaches, since practitioners of each have much to learn from the other. Mechanics
of Materials, with its emphasis on physical reasoning and a full exploration of the
practical consequences of the results, is often able to provide insights into the problem
that are less easily obtained from a purely mathematical perspective. Indeed, we
shall make extensive use of physical parallels in this book and pursue many problems
to conclusions relevant to practical applications, with the hope of deepening the
reader’s understanding of the underlying structure of the subject. Conversely,
