Penalty-Based Solution for the Interval Finite-Element Methods

A new approach for achieving guaranteed reliable results within the context of finite-element approximation of mechanical systems is developed. A reliable analysis requires that all the sources of uncertainty and errors be accommodated. The appropriateness of a partial differential equation to a given physical problem is beyond the scope of this work. Parameter uncertainty is treated as intervals in this work and guaranteed bounds on the "unknown" true solutions are obtained. In this paper an element-by-element penalty-based interval finite-element analysis of linear elastic structural mechanics and solid mechanics problem is introduced. Material and load uncertainties are handled simultaneously. Presented numerical examples illustrate the ability of the method to maintain very sharp solution enclosures even when the number of the interval parameters or the size of the problems is increased.