Non-deterministic 'possibilistic' approaches for structural analysis and optimal design - A comparison of numerical methods for computing structural response uncertainties

Abstract

The development of methods to take into account uncertainties in structural analysis computations and in design optimization procedures is attracting a fast growing interest from both the scientific and the industrial communities. In this domain, possibilistic methods in which uncertainties are defined by fuzzy numbers appears as an alternative to the classical probabilistic methods like the MonteCarlo simulations or the Statistical Finite Element Method. The principal difficulty of possibilistic methods is that they lead to solve systems of equations in which the coefficients are defined by intervals. The paper presents and compares several approaches for the direct solution of such intervals linear equations systems. The Vertex method is taken as reference. It is shown that the problems which are solved are mathematically different according to the method used. For static linear analysis, a cost-effective iterative solution of the Vertex is proposed. It is based on Neumann series expansions and solves an optimization sub-problem so as to compute extrema of the structural responses. Effectiveness of the method is illustrated by the solution of truss problems, classical in the optimization literature. Extension of the method to inverse problems of design is also considered.