TABLE OF CONTENTS Real mechanical systems generally comprise an assembly of deformable solids, which must be modelled within the framework of the theory of continuum mechanics. Accordingly, material is assumed to be distributed continuously in a 3D domain. However, in most instances, the engineer deals with structural elements endowed with geometrical particularities which allow for further simplification in modelling, based on the concept of 2D or even 1D equivalent continuous media. Before embarking on the presentation of such models, which is the central object of this book, it is appropriate to review first a few fundamental concepts, definitions and laws of continuum mechanics. This vast subject is restricted here to a few important aspects of linear elasticity and elastodynamics of solids.
The mechanics of solid bodies is concerned with the motion of deformable media, in which solid matter is continuously distributed over a domain of the three-dimensional Euclidean space, bounded in every direction. Accordingly, it extends the mechanics of discrete particles, dealing with the new following aspects:
To describe the motion, use is made of an infinite, and even more significant, an uncountable set of degrees of freedom (DOF). The three displacement components of all material points define a vector field 
( 
; t), which is a continuous and differentiable function of the position vector and depends on time t. A priori, ( ; t) and are defined in a 3D Euclidean space. Assumption of continuity of ( ; t) implies that...
