دانلود کتاب Three Dimensional Problems of the Theory Elasticity

Introduction to English Edition

This book, which was first published in Russian in 1955, treats the
solution of certain classical problems of the mathematical theory of
elasticity. Beside the revised derivation of previously known solutions,
it presents material on three-dirnensional problems of the theory of
elasticity published by the author over the past years.

Assuming that the reader is familiar with the general foundations of
the mathematical theory of elasticity and the solution of the simplest
problems, the author has concentrated attention on more specialized
questions; they have been enumerated in the Contents, and make repeti-
tion here superfluous. The author has striven to give an independent
exposition of the separate chapters. However, a uniformity of method
has been maintained, namely the representation of the solutions in terms
of the Papkovich-Neuber harmonic functions. In many cases, this per-
mits a systematic derivation of the solutions and the avoidance of "guess-
ing" and trial substitujions, from which success can be expected only if
one has already sufficient experience in the solution of complicated
boundary-value probÍems. The method of Papkovich-Neuber is not used
in Chapters 3 and 4, because the application of the symbolic method
adopted in these chapters to the displacement equations of equilibrium
in the theory of elasticity leads more quickly to the representation of the
solutions of problems concerning the elastic layer and plate.

Of course, the book does not give a complete coverage of the topic;
there is no treatment of the questions of existence of solutions and the
application of integral equations, no exposition of the problems of Saint
Venant, or of Michell and Almansi on the deformation of prismatic beams.
Together with other omissions, the reader will also find no account of the
excellent achievements of H. Neuber on the problem of stress concentra-
tion in notches and cavities.

The German translation of the book appeared in 1963 (Akademie-
Verlag, Berlín).
Leningrad, 1963
A. I. LUR'E