## Theoretical ElasticityThis highly regarded hardcover engineering manual is mainly concerned with three important aspects of elasticity theory: finite elastic deformations, complex variable methods for two-dimensional problems for both isotropic and aeolotropic bodies, and shell theory. Also discussed are three-dimensional problems for isotropic and transversely isotropic bodies. Chapter 1, devoted to mathematical preliminaries, includes a summary of tensors for workers unfamiliar with those notations. Subsequent chapters deal with the general theory of elasticity for finite deformations, solutions of a number of special problems, mostly for incompressible isotropic bodies, a theory of small deformations superposed on finite deformations, classical infinitesimal theory of elasticity, the theory of plane strain, plate theory, plane problems for isotropic bodies, and for aeolotropic bodies. The last chapters, 10-16, are devoted to the theory of shells. For this second edition, the authors added material on thermodynamics, as well as a new chapter dealing with methods of deriving membrane theory, inextensional theory, and bending theory, by asymptotic expansions of the three-dimensional linear elastic equations |

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A. E. Green applied stress arbitrary assume axes base vectors bending theory body Bo body forces boundary conditions boundary-value problem Chapter Christoffel symbols circle circular hole cłł coefficients complex potentials consider contour contravariant corresponding cosh Covariant and contravariant covariant derivatives covariant differentiation cylinder defined deformed denoted displacement vector elastic potential equations of equilibrium finite formulae given half-plane Hence holomorphic holomorphic functions incompressible inextensional integral isolated force isotropic isotropic bodies membrane theory metric tensor middle surface mixed tensor notation obtained plane strain plate Proc region respect resultant force satisfied scalar shearing shell sinh solution strained body stress couples stress resultants stress tensor stress—strain relations stresses and displacements stresses and rotation symmetric tensor of order transformation unit normal unstrained values vanish at infinity zero