Fuzzy Boundary Element Method for Geometric Uncertainty in Elasticity Problem

Solutions to partial differential equations describing behavior of physical systems are often imprecise. This uncertainty is due to numerical approximations and uncertainty in physical parameters. In elastostatics, these parameters include uncertain material behavior, uncertain boundary conditions, and uncertain geometry of the system. This paper addresses the treatment of geometrical uncertainty for elasticity problems. The new method predicts fuzzy responses for the given membership functions, describing the range of tolerances for the system’s geometry. To obtain exact bounds on the solution to the resulting fuzzy linear system of equations, fuzzy matrix parameterization is developed. Numerical example is shown to illustrate the behavior of the method.