Interval Objects and Operations in Deformable Solid Mechanics Problems

Boyarshinov M.G.

In constructing interval vectors and tensors, the requirement of invariance of these objects under transformation of the system of coordinates is taken into account. For illustrations, interval scalars, vectors, and tensors are used in solving the simplest engineering problems of deformable solid mechanics to construct distributions of displacements, strains, and stresses, including residual ones, satisfying the conditions of elastic adaptivity (J. Zarka methods).

DESSOMBZ O., THOUVEREZ F., LAÎNÉ J.-., JÉZÉQUEL L.

This paper addresses the problem of mechanical systems in which parameters are uncertain and bounded. Interval calculation is used to find an envelope of transfer functions for mechanical systems modelled with finite elements. Within this context, a new formulation has been developed for finite element problems involving bounded parameters, to avoid the problems of overestimation. An iterative algorithm is introduced, which leads to a conservative solution for linear mechanical problems. A method to ensure the convergence of this algorithm is also proposed. This new algorithm has been tested on simple mechanical systems, and leads to a conservative envelope of the transfer functions.

Birdie T.R., Surana K.S.

Hydrological data are often highly inaccurate. Interval methods help to estimate inaccuracy caused by data uncertainty, both for forward problems (in which we predict how water will flow in the known medium), and for the inverse problems (in which we observe how water flows and determine the properties of the medium).