Vera-Laboy, John A.

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    Instabilities in three-dimensional solids
    (2007-11) Vera-Laboy, John A.; Godoy, Luis A.; College of Engineering; López, Ricardo R.; Cáceres, Arsenio; Acosta, Felipe J.; Department of Civil Engineering; Shafiq, Basir
    This thesis presents an investigation of the buckling phenomenon and the consequences of stability theory for three-dimensional, thick solids. The theme structures considered are solid cylinders under axial compression. An analytical formulation using a linear fundamental path and an incremental displacement field is derived, leading to an eigenvalue problem. Bifurcation analyses are performed on the simplified analytical model for a variety of isotropic linear-elastic materials. Results predict bifurcations for very high deformations in modes that display a wavy pattern on the external surfaces of the cylinder. Bifurcation analyses are also performed using a general purpose finite element program. Predicted bifurcations are confirmed to appear at large deformation levels. Limit points for solid structures are also investigated with geometrically nonlinear analyses. Results show that limit point instabilities are found at smaller displacement levels than the bifurcations. A reduced energy method is developed in the thesis to obtain a lower bound to buckling loads in this problem. Earlier developments in lower bound approaches to stability problems were directed towards the buckling of thin-walled structures. The reduced energy method is applied to the solid buckling problem using the analytical formulation. Results show reasonable agreement between the reduced methodology developed and the finite element nonlinear analyses, but not lower bounds. Imperfection sensitivity, inferred from the bifurcation analysis results, is also studied. Buckling modes obtained from the finite element bifurcation analyses are imposed as imperfections on the initial geometry of the solids and nonlinear analyses are performed. Results indicate reduced displacement capacity. The effect of imperfection amplitude is also studied. Increasing amplitude is shown to lower displacement capacity of the solid, though limitations of the finite element analyses become apparent at larger imperfection amplitudes. Finally, the behavior of solid three-dimensional cylinders made with nonlinear elastic materials, foams, is investigated, to elucidate the influence of material nonlinearity on the response. Results indicate that the phenomena investigated in this thesis holds for models of such materials as well.