Jürgen Garloff, Andrew P. Smith, Horst Werkle

HTWG (University of Applied Sciences) Konstanz

Finite element models for mechanical truss structures, where all
of the physical model parameters are uncertain are considered.
Not just the material values and applied loads, but also the positions
of the nodes, are assumed to be inexact but bounded and are
represented by intervals. In this case the application of the finite
element method results in a system of linear equations with
numerous interval parameters exhibiting nontrivial dependencies
which cannot be solved conventionally.
We have previously employed a general-purpose iterative solver for
parametric systems of equations provided by E. Popova, coupled with
software for enclosing the range of multivariate polynomials arising
in the parameter dependencies, to solve problems in the case of
uncertain material values and loads only.
With the addition of interval pruning techniques, simple problems
with uncertain node locations have also been solved. With the further
addition of a monotonicity analysis of all the parameters, we aim to
provide tight guaranteed enclosures for the element forces and
node displacements for a larger class of finite element models.