In this thesis we consider the eversion and bifurcation of both incompressible and compressible isotropic elastic cylinders. To begin we give a brief account of the basic equations of non-linear elasticity. We then study the basic eversion of hollow cylinders composed of both incompressible and compressible material for a variety of strain-energy functions and offer some analysis for the existence and uniqueness of the cylindrical everted state achieved. Next we study the effect of applying an incremental deformation to the basic everted state and formulate the bifurcation problem with the undeformed thickness ratio as a parameter. We study the bifurcation problem in detail for a variety of strain-energy functions and consider the effects of compressibility, initial tube thickness and mode numbers on the bifurcation produced. The bifurcation problems are solved numerically and we use tlie present problem to study two different numerical methods. We find that the standard determinental method, extensively used in the past for elastic bifurcation problems, is not adequate for the problems considered in this thesis and thus adopt the Compound Matrix method. We compare both methods and give a derivation of the Compound Matrix method.
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