Theory of Elasticity - Lurie, A. I.; Belyaev, Alexander; SpringerLink (Online service) (Berlin, Heidelberg : Springer Berlin Heidelberg, 2005)
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.
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$1 (Bs 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.s
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