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Some partial solutions of finite elasticity

Elastic deformations beyond the range of the classical infinitesimal theory of elasticity are governed by highly non-linear partial differential equations and in general there exists no clear statement of these equations which does not involve stress components. Orthodox methods of solution are not usually applicable and consequently only a few exact solutions are known. In this thesis for some special classes of deformations and for some special materials we obtain substantial new reductions of the equilibrium equations which involve the deformation only. From these reduced equilibrium equations a number of new exact partial solutions are derived for the neo-hookean and Mooney materials.