A Treatise On The Mathematical Theory Of Elasticity

An indispensable reference work for engineers, mathematicians, and physicists, this book is the most complete and authoritative treatment of classical elasticity in a single volume. Beginning with elementary notions of extension, simple shear and homogeneous strain, the an­analysis rapidly undertakes a development of types of strain, displacements corresponding to a given strain, cubical dilatation, and composition of strains. A detailed analysis of stress including the stress quadric and uniformly varying stress leads into an exposition of the elasticity of solid bodies. Based upon the work-energy concept, experimental results are examined and the significance of elastic constants in general theory considered. Hooke’s Law, elastic constants, methods of determining stress, thermo-elastic equations, and other topics are carefully discussed. The relation between the mathematical theory of elasticity and technical mechanics is covered and the limitations of the mathematical theory set forth. The equilibrium of isotropic elastic solids is treated by Saint-Venant’s principle and the equilibrium of aeolotropic solid bodies is treated by considerations of symmetry of structure. Detailed consideration is given to the nature of the transmission of force and Hertz’s theory of impact, two-dimensional elastic systems and Volterra’s theory of dislocations. The theory of an elastic sphere is related to tidal, rotational and gravitational effects on the earth and the propagation of waves in elastic solid media related to the propagation of light. A minutely detailed treatment of the bending of beams under varying conditions, the general theory of bending, twisting and equilibrium of thin rods, vibration of rods, the stretching and bending of plates, the deformation of curved plates and buckling effects occupies the second half of the volume.