Theory of Elasticity

This invaluable treatise belongs to the cultural heritage of mechanics. It is an encyclopaedia of the classic and analytic approaches of continuum mechanics and of many domains of natural science. The book is unique also because an impressive number of methods and approaches it displays have been worked out by the author himself. In particular, this implies a full consistency of notation, ideas and mathematical apparatus which results in a unified approach to a broad class of problems. The book is of great interest for engineers who will find a lot of analytical formulae for very different problems covering nearly all aspects of the elastic behavior of materials. In particular, it fills the gap between the well-developed numerical methods and sophisticated methods of elasticity theory. It is also intended for researchers and students taking their first steps in continuum mechanics as it offers a carefully written and logically substantiated basis of both linear and nonlinear continuum mechanics.

Zusammenfassung
The classical theory of elasticity maintains a place of honour in the science ofthe behaviour ofsolids. Its basic definitions are general for all branches of this science, whilst the methods forstating and solving these problems serve as examples of its application. The theories of plasticity, creep, viscoelas­ ticity, and failure of solids do not adequately encompass the significance of the methods of the theory of elasticity for substantiating approaches for the calculation of stresses in structures and machines. These approaches constitute essential contributions in the sciences of material resistance and structural mechanics. The first two chapters form Part I of this book and are devoted to the basic definitions ofcontinuum mechanics; namely stress tensors (Chapter 1) and strain tensors (Chapter 2). The necessity to distinguish between initial and actual states in the nonlinear theory does not allow one to be content with considering a single strain measure. For this reason, it is expedient to introduce more rigorous tensors to describe the stress-strain state. These are considered in Section 1.3 for which the study of Sections 2.3-2.5 should precede. The mastering of the content of these sections can be postponed until the nonlinear theory is studied in Chapters 8 and 9.

Inhalt
Basic concepts of continuum mechanics.- Stress tensor.- Deformation of a continuum.- Governing equations of the linear theory of elasticity.- The constitutive law in the linear theory of elasticity.- Governing relationships in the linear theory of elasticity.- Special problems of the linear theory of elasticity.- Three-dimensional problems in the theory of elasticity.- Saint-Venant's problem.- The plane problem of the theory of elasticity.- Basic relationships in the nonlinear theory of elasticity.- Constitutive laws for nonlinear elastic bodies.- Problems and methods of the nonlinear theory of elasticity.