Visualizing displacements and stresses that were calculated using interval methods and finite elements for a system with uncertainty in forces and geometry
Interval methods are currently one of three methods available to model uncertainty in a system. In this thesis interval methods along with finite elements were used to model the uncertainty in beams and a square plate. Intervals defined the upper and lower bounds of uncertain lengths, widths and forces. Care had to be taken to reduce the dependency in the equations in order to obtain sharper bounds on the solution. Using the symbolic notation in Matlab, sharper bounds were calculated for the displacements and the stresses. The life and reliability of the system were computed using stochastic methods. The results were then displayed in the virtual environment. The virtual reality program contains a menu option that allows the user to change the reliability of the part, the life, the applied stress, the stress deviation, the force and the tolerance and observe the resulting stress distribution and displacements on the square plate. The plate was also shown with neighboring pieces so that a designer could view the gap between the displaced square plate and the nearest neighboring part
