In comparison to metallic materials, ceramic materials are very brittle which has made a wide use of them difficult up to now. For this reason, stochastic failure criteria, which differ considerably from those of ductile materials, have to be formulated and calculated mathematically. Because of high specific elasticity and stiffness properties, the ceramics are suitable for the layout of rotating components with a high rotating velocity. In order to find the optimal layout of a component made of ceramic materials, a stochastic optimization problem has to be defined and solved.
A ceramic turbine disk has been chosen to demonstrate the shape optimization and the application of the stochastic optimization. By means of the functional-efficient boundaries and the associated optimal contours of the component conventional ductile materials are compared with ceramics for this application example. Herewith, the range of application of the materials examined can be determined.