Fuzzy behavior of mechanical systems with uncertain boundary conditions

Abstract

The problem of structures' sensitivities to uncertain boundary conditions is presented in this paper and the effect of uncertain prescribed displacements on the static response of structures is discussed. The imprecise or uncertain prescribed displacements are treated as fuzzy quantities with known membership functions. For numerical computations, a fuzzy quantity can be approximated by sets of closed intervals with respect to specified α-cuts. This transforms the problem into a set of interval equations at each α-level. A numerical method is developed to solve the system of fuzzy equations. Simple stress analysis is also used to establish and illustrate the method. A numerical example is presented to demonstrate the capability of the method.