Non-Deterministic Methods for Product/Process Analysis and Robust Design — the “Possibilitic” Approach

The development of methods to take into account uncertainties in structural analysis computations and in design optimisation procedures is attracting a fast growing interest from both the scientific and the industrial communities. Possibilistic methods in which uncertainties are represented by fuzzy numbers appear as an alternative to the classical probabilistic methods like the Monte-Carlo methods or the Statistical Finite Element Method. The principal difficulty of possibilistic methods is that they lead to the solutions of systems of equations whose coefficients are defined by intervals. The following paper presents several approaches for the solution of such systems, some of them original, taking the Vertex engineers’ method as reference. Extension of these methods to inverse design problems is considered.