The problem that is addressed here is that of a circular thin plate clamped peripherally with frictionless contact to an elastic sphere. A complete and effective solution to this problem is developed to describe the relationship between the contact force and the relative penetration. Analysis of the contact stress and surface displacements of the plate and the sphere is carried out. Comparison of the results with the Hertz theory indicates that the former predicts relative penetration with more accuracy, which indicates that the Hertz theory is not applicable to the elastic sphere in contact with the circular thin plate with a large deformation. In addition, the results of the theoretical model show good agreement with the ANSYS simulation results.
Propellant Gauging is of vital importance to a spacecraft at the end of its life. Based on the Monte Carlo Method, uncertainty analysis and the improvement of propellant gauging using gas injection have been studied. As a result of the analysis, the gauging uncertainty has weak relation to the uncertainties of the volumes of the injection room and tank, the uncertainties of the pressure, and the temperature in the injection room. Relatively, the uncertainties of the temperature and pressure in the tank have a great effect on the gauging uncertainty. By improving the uncertainties of the tank pressure and temperature within 0.04% and 0.4%, the final gauging uncertainty can be obtained within 0.4%. Ground tests have been conducted and the results came out with approximately 0.4% error, well within the theoretical analysis.