Abstract:

The objective of this research has been to develop accurate solutions to problems involving end-loaded cylinders. This was achieved through an extended application of a semi-analytic method of analysis, which enabled the consideration of fairly general loading cases and domain geometries.

The first part of this study offers three-dimensional solutions for extension, bending, torsion and flexure problems--collectively referred to as Saint-Venant's problems--of prismatic, yet inhomogeneous, cylinders with arbitrary cross-sectional shapes and the most general form of anisotropy.

The second part makes use of an eigenfunction expansion of the cross-sectional deformations of the cylinder, again afforded by the said semi-analytic method, and explores the treatment of self-equilibrated end tractions, prescribed pointwise. This capability is exploited in the investigation of the decay lengths of inter-laminar stresses in layered composites, and of the transition effects in connected cylinders with non-matching cross-sectional shapes and material constitution.

The final part of this dissertation is devoted to the development of a refined, Timoshenko-like, beam theory for static and dynamic analyses of homogenous cylinders. The semi-analytical approach is combined with an energy method to obtain accurate shear-correction coefficients of cross-sections with arbitrary geometry. These results constitute significant improvements over existing approaches, and are extendable to inhomogenous anisotropic cylinders as well as laminated plates.

All three parts of this study include rigorous verification problems, whereby the obtained results are satisfactorily checked against exact--whenever this was possible--and three-dimensional finite element solutions.