The Stroh formalism is a powerful and elegant mathematical
method developed for the analysis of the equations of anisotropic
elasticity. The purpose of this exposition is to introduce the
essence of this formalism and demonstrate its effectiveness in both
static and dynamic elasticity. The equations of elasticity are
complicated, because they constitute a system and, particularly for
the anisotropic cases, inherit many parameters from the elasticity
tensor. The Stroh formalism reveals simple structures hidden in the
equations of anisotropic elasticity and provides a systematic
approach to these equations.
This exposition is divided into three chapters. Chapter 1 gives
a succinct introduction to the Stroh formalism so that the reader
can grasp the essentials as quickly as possible. In Chapter 2
several important topics in static elasticity, which include
fundamental solutions, piezoelectricity, and inverse boundary value
problems, are studied on the basis of the Stroh formalism.
Chapter 3 is devoted to Rayleigh waves, for long a topic of
utmost importance in nondestructive evaluation, seismology, and
materials science. There we discuss existence, uniqueness, phase
velocity, polarization, and perturbation of Rayleigh waves through
the Stroh formalism.
This work will appeal to students and researchers in applied
mathematics, mechanics, and engineering science.
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