Tube hydroforming process is a relatively new technology compared to conventional manufacturing via stamping and welding. However there is not much knowledge available for the product or process designers. The objective of this study will determine the flow stress and forming limit diagram of tubular materials to discuss the formability of tubes. Firstly, a mathematical model is proposed to examine the plastic deformation behavior of a thin-walled tube at different process parameters during the bulge hydroforming process without axial feeding. In the formulation of this mathematical model, an ellipsoidal surface and non-uniform thinning in the free bulged region and sticking friction between the tube and die are assumed. In the sticking friction mode, the elements after contact with the die do not move or slide. The effects of various forming parameters, such as the die entry radius, the bulge length, anisotropy, the initial thickness of the tube, etc., upon the forming pressures are discussed systematically. Secondly, an analytical model combined with hydraulic bulge tests is proposed to evaluate the properties of tubular materials considering anisotropy effect. Annealed AA6011 aluminum tubes and SUS409 stainless steel tubes are used for the bulge test. The tube thickness and radius at the pole and the internal forming pressure are measured simultaneously during the bulge test. The anisotropic values are obtained from tensile tests. From above experimental data, the effective stress - effective strain relations can be derived by this analytical model. The finite element method is used to conduct the simulations of hydraulic bulge forming with the flow stresses obtained by the above-mentioned model. The analytical forming pressures versus bulge heights are compared with the experimental results to validate the approach proposed in this study. Finally, this study also establishes the Forming Limit Diagram (FLD) of aluminum tubular material. An experimental system of tube hydroforming in which axial feed is applied to carry out the hydraulic bulge-forming test of the annealed aluminum alloy tubes. Furthermore, Hill¡¦s new yield criterion is also used to predict the Forming Limit Curves of sheets. The predicted forming limit diagrams are compared with the experimental data. The results of this study can provide useful knowledge for process design. In addition, the process parameters of flow stress and forming limit diagram obtained can improve the accuracy of the simulation results in industrial and academic fields.

In general relativity, the nature of mass is non-local. However, an appropriate def-inition of mass at a quasi-local level could give a more detailed characterization ofthe gravitational field around massive bodies. Several attempts have been made tofind such a definition. One of the candidates is the Hawking mass. This thesispresents a method for calculating the spin coefficients used in the expression for theHawking mass, and gives a closed-form expression for the Hawking mass of ellipsoidal2-surfaces in Minkowski spacetime. Furthermore, the Hawking mass is shown to havethe correct limits, both in Minkowski and Schwarzschild, along particular foliationsof leaves approaching a metric 2-sphere. Numerical results for Schwarzschild are alsopresented.

<p>In general relativity, the nature of mass is non-local. However, an appropriate def-inition of mass at a quasi-local level could give a more detailed characterization ofthe gravitational field around massive bodies. Several attempts have been made tofind such a definition. One of the candidates is the Hawking mass. This thesispresents a method for calculating the spin coefficients used in the expression for theHawking mass, and gives a closed-form expression for the Hawking mass of ellipsoidal2-surfaces in Minkowski spacetime. Furthermore, the Hawking mass is shown to havethe correct limits, both in Minkowski and Schwarzschild, along particular foliationsof leaves approaching a metric 2-sphere. Numerical results for Schwarzschild are alsopresented.</p>

The aim of this diploma thesis is to design a suitable reflector concentrating a light beam into a circular hole in a gobo. The light beam behind the screen should have good efficiency and at the same time good homogeneity. For the reflector design and analysis a software for designing optical systems called LightTools was used. The reflector was designed by six different methods. Several smooth and several faceted reflectors were designed. The selected reflector was analyzed in combination with a varifocal lens. For selected reflector was designed mechanical store with respect to the anticipated operating conditions. This thesis serves as the basis for the producing of the reflector.