Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Department of Aeronautics and Astronautics

First Advisor

Anthony N. Palazotto, PhD


A two-dimensional, geometrically and materially nonlinear shell theory applicable to arbitrary geometries described by orthogonal curvilinear coordinates and encompassing large displacements, moderate rotations for large strain situations has been developed. Additionally, the theory includes Jacobian transformation matrices, based upon displacement parameters, for the Cauchy - 2nd Piola-Kirchhoff stress-state and the Cauchy (Almansi) - Green strain-state transformations, and a layered material approach is included for the elastoplastic analysis to allow for variation of plasticity through-the-thickness. Doubly curved 20, 28, and 36 degree-of-freedom finite elements are defined based on specialization of the theory to spherical coordinates. The computer program includes algorithms for linear and nonlinear problems. Post-collapse nonlinear solutions are found through a displacement-control incrementation scheme. This provides solutions to classical von Karman flat plate and Donnell spherical shell equations, intermediate von Karman flat plate and Donnell spherical shell equations, and large displacement and moderate rotational formulations. For deep shells exhibiting large rotations and displacements over 15-20% of the shell's surface, the Lagrangian constitutive relations (including the Jacobian transformation matrices for the stress- and strain-states) should be included to accurately reflect the variation of the material coordinate system with respect to the structural axis system. For those plates and shells exhibiting large strains, along with large rotations and displacements over 15-18% of the outer surface, plasticity should be included in the model.

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