Due to most studies on vibration of pre-loaded rectangular plate being subject to uniform loading, this thesis will investigate vibration of plate under preloading with sine functional distributions. The approach behind this study is using first-order shear deformation plate theory and finite element method to analyze vibration frequency. Study results show that, when a plate¡¦s boundary condition is CCCC, SSSS, CFCF, or SFSF with sine functional pre-loading, its vibration frequency will increase to an extent with little difference when the number of modes increases. Vibration frequency will increase shortly then decrease when increasing the number of sine waves. Vibration frequency will also increase when increasing stress parameters. However, obvious frequency changes are observed only at lower modes with SFSF boundary condition.

Mechanical stresses placed on ferromagnetic materials while under the influence of a magnetic field are known to cause changes to the permanent magnetization of the material. Modeling this phenomenon is vital to the safety of ocean faring ships. In this thesis, a quasi-strip theory method of computing the nonlinear wave induced motion of a ship is developed, and the fluid pressure on the surface of the hull is used to determine the mechanical stresses. An existing magnetostatic volume integral equation code is used to evaluate the effects of the ship motion and hull stresses. The resulting changes in the magnetic field for various ship forms are presented to demonstrate the effects of given sea states.

ABSTRACT In the present study, it is emphasized that mixed-type finite element formulation, which is different from the conventional displacement-type formulation, has both displacements and stresses as its primary variables. Therefore, stress, as well as displacement boundary conditions, can be imposed easily and exactly. Except around the outer edge where support is placed, stresses obtained by both displacement and mixed formulation are close to each other when the circular plate is subject to transverse uniform loading. However, large discrepancies exist around the locations of constraints, where the stresses are always significant and critical. Since mixed formulation of the present study can completely satisfy the stress and displacement boundary conditions, it can theoretically provide more accurate stress analysis and should be considered as a more appropriate analysis tool.