The geometrically nonlinear constant moment triangle based on the von Karman theory of thin plates is first described. This finite element, which is believed to be the simplest possible element to pass the totality of the von Karman patch test, is employed throughout the present work. It possesses the special characteristic of providing a tangent stiffness matrix which is accurate and without approximation. The stability of equilibrium of discrete conservative systems is discussed. The criteria which identify the critical points (limit and bifurcation), and the method of determination of the stability coefficients are presented in a simple matrix formulation which is suitable for computation. An alternative formulation which makes direct use of higher order directional derivatives of the total potential energy is also presented. Continuation along the stable equilibrium solution path is achieved by using a recently developed Newton method specially modified so that stable points are points of attraction. In conjunction with this solution technique, a branch switching method is introduced which directly computes any intersecting branches. Bifurcational buckling often exhibits huge structural changes and it is believed that the computation of the required switch procedure is performed here, and for the first time, in a satisfactory manner. Hence, both limit and bifurcation points can be treated without difficulty and with continuation into the post buckling regime. In this way, the ability to compute the stable equilibrium path throughout the load-deformation history is accomplished. Two numerical examples which exhibit bifurcational buckling are treated in detail and provide numerical evidence as to the ability of the employed techniques to handle even the most complex problems. Although only relatively coarse finite element meshes are used it is evident that the technique provides a powerful tool for any kind of thin elastic plate and shell problem. The thesis concludes with a proposal for an algorithm to automate the computation of the unknown parameter in the branch switching method.

The settling of spherical and cylindrical particles in a linearly stratified fluid is investigated using experiments. The double-tank method is used to generate a linear stratification with a red colored dye homogeneously mixed in the heavy water tank. As a result of feeding the stratification using dyed heavy water, the concentration of dye varies with depth in the experiment tank. A powerful back-light and a digital camera are used to record the events. Assuming the concentration of dye is directly proportional to density of fluid, Beer-Lambert's law is used to generate a calibration between intensity of the light measured by the camera and density of the fluid. Using this calibration, density is evaluated in all the images captured. In the parameter space of this study, the spheres have three different wake patterns. The area of fluid disturbed by a suspension of spheres increases with <i>Re</i> and <i>Fr</i>. As a result, the amount of energy available for the mixing and the irreversible change of total potential energy in the system increases with <i>Re</i>, <i>Fr</i> and number of particles. Cylinders drag volumes of light fluid to larger depths in their wake than spheres and shed the light fluid in the form of vortices. This results in lower volumes of fluid perturbed by the cylinders. However, as the light fluid is dragged to larger depths, the amount of energy generated for mixing and the change in total potential energy of the system is higher. Spheres are thus more efficient in disturbing volumes of fluid but cylinders are more efficient in causing irreversible changes to the state of the system.