IPIES for Uncertainly Defined Shape of Boundary, Boundary Conditions and Other Parameters in Elasticity Problems

The main purpose of this paper is modelling and solving boundary value problems simultaneously considering uncertainty of all of input data such as: shape of boundary, boundary conditions and other parameters. The strategy is presented on the basis of problems described by Navier-Lamé equations. Therefore, the uncertainty of parameters here, means the uncertainty of the Poisson’s ratio and Young’s modulus. For solving uncertainly defined problems we use implementation of interval parametric integral equations system method (IPIES). In this method we propose modification of directed interval arithmetic for modeling and solving uncertainly defined problems. We consider an examples of uncertainly defined, 2D elasticity problems. We present boundary value problems with linear as well as curvelinear (modelled using NURBS curves) shape of boundary. We verify obtained interval solutions by comparison with precisely defined (without uncertainty) analytical solutions. Additionally, to obtain errors of such solutions, we decided to use the total differential method. We also analyze influence of input data uncertainty on interval solutions.