Теория упругости

The classical theory of elasticity retains its place of honor in the science of the behavior of a deformable solid. Its initial definitions are common to all branches of this science, and methods for posing and solving problems serve as models for it. The successes and achievements of the theory of plasticity, creep, elastic-viscous media, and fracture of solids do not obscure the importance of the methods of the theory of elasticity for substantiating methods for calculating the stress state in building structures and machines, which constitute an essential part of the sciences of strength of materials and structural mechanics.

The first two chapters (Part I) are devoted to the basic definitions of continuum mechanics - stress tensors (Chapter I) and strain tensors (Chapter II). The need to distinguish in a nonlinear theory the initial and final states of a medium does not allow one to be content with considering only one measure (or tensor) of deformation, and in this regard, it turns out to be advisable to introduce tensors that are different from each other in the description of the stressed state. These issues are discussed in § 3 of Chapter. I, the study of which should be preceded by the study of §§ 3-5 ch. II. The assimilation of the contents of these paragraphs can be postponed without prejudice until the study of nonlinear theory (in Chapters VIII, IX).