Mechanics of Solids: Volume II: Linear Theories of Elasticity and Thermoelasticity, Linear and Nonlinear Theories of Rods, Plates, and Shells

Reissue of Encyclopedia of Physics / Handbuch der Physik, Volume VIa The mechanical response of solids was first reduced to an organized science of fairly general scope in the nineteenth century. The theory of small elastic deformations is in the main the creation of CAUCHY, who, correcting and simplifying the work of NAVIER and POISSON, through an astounding application of conjoined scholarship, originality, and labor greatly extended in breadth the shallowest aspects of the treatments of par­ ticular kinds of bodies by GALILEO, LEIBNIZ, JAMES BERNOULLI, PARENT, DANIEL BER­ NOULLI, EULER, and COULOMB. Linear elasticity became a branch of mathematics, culti­ vated wherever there were mathematicians. The magisterial treatise of LOVE in its second edition, 1906 - clear, compact, exhaustive, and learned - stands as the summary of the classical theory. It is one of the great "gaslight works" that in BOCHNER'S words! "either do not have any adequate successor[ s] . . . or, at least, refuse to be super­ seded . . . ; and so they have to be reprinted, in ever increasing numbers, for active research and reference", as long as State and Society shall permit men to learn mathe­ matics by, for, and of men's minds. Abundant experimentation on solids was done during the same century. Usually the materials arising in nature, with which experiment most justly concerns itself, do not stoop easily to the limitations classical elasticity posits.

Table of Contents:
The Linear Theory of Elasticity.- A. Introduction.- B. Mathematical preliminaries.- C. Formulation of the linear theory of elasticity.- D. Elastostatics.- E. Elastodynamics.- References.- Linear Thermoelasticity.- A. Introduction.- B. The foundations of the linear theory of thermoelasticity.- C. Equilibrium theory.- D. Dynamic theory.- List of works cited.- Existence Theorems in Elasticity.- 1. Prerequisites and notations.- 2. The function spaces $$\mathop H\limits^ \circ$$m and Hm.- 3. Elliptic linear systems. Interior regularity.- 4. Results preparatory to the regularization at the boundary.- 5. Strongly elliptic systems.- 6. General existence theorems.- 7. Propagation problems.- 8. Diffusion problems.- 9. Integro-differential equations.- 10. Classical boundary value problems for a scalar 2nd order elliptic operator.- 11. Equilibrium of a thin plate.- 12. Boundary value problems of equilibrium in linear elasticity.- 13. Equilibrium problems for heterogeneous media.- Boundary Value Problems of Elasticity with Unilateral Constraints.- 1. Abstract unilateral problems: the symmetric case.- 2. Abstract unilateral problems: the nonsymmetric case.- 3. Unilateral problems for elliptic operators.- 4. General definition for the convex set V.- 5. Unilateral problems for an elastic body.- 6. Other examples of unilateral problems.- 7. Existence theorem for the generalized Signorini problem.- 8. Regularization theorem: interior regularity.- 9. Regularization theorem: regularity near the boundary.- 10. Analysis of the Signorini problem.- 11. Historical and bibliographical remarks concerning Existence Theorems in Elasticity.- The Theory of Shells and Plates.- A. Introduction.- B. Kinematics of shells and plates.- C. Basic principles for shells and plates.- D. Elastic shells.- E. Linear theory of elastic plates and shells.- F. Appendix: Geometry of a surface and related results.- References.- The Theory of Rods.- A. Introduction.- B. Formation of rod theories.- C. Problems for nonlinearly elastic rods.- References.- Namenverzeichnis. — Author Index.- Sachverzeichnis (Deutsch-Englisch).- Subject Index (English-German).