This treatise on the mathematical theory of elasticity is divided into seven major parts. Part 1 deals with the fundamental equations of the mechanics of an elastic body. It includes separate chapters on analyses of stress and strain, relation between stress and strain, the equilibrium equations of an elastic body, and the fundamental boundary value problems of static elasticity. Part 2 treats planar problems whose solutions are obtained with the aid of the stress function and its complex representation. The technique of conformal mapping is introduced. Part 3develops the Fourier series approach to the solution of planar problems, while Parts 4 and 5 make use of Cauchy integrals. Part 6 presents solutions for special planar geometries and Part 7 deals with the extension, torsion and bending of bars.
Novozhilov, V. V., Thin Shell Theory (P. Noordhoff, Groningen, 1964), 377pages. A mathematical analysis of stresses and strains in thin shells using linear elasticity theory. There are four chapters on the general theory of thin elastic shells, the membrane theory of shells, cylindrical shells, and shells of revolution.
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