Improved interval finite element for analysis of planar frames

The Interval Finite Element Method (IFEM) can be used for the analysis of structures with uncertainties in load, geometry, and material. However, a naive application of IFEM leads to meaningless overestimated enclosures due to interval dependency. In this work, a new finite element solution for planar frames under interval uncertainties is introduced. In particular, for a beam element, we present a new decomposition of the stiffness matrix that yields a significant reduction of overestimation. The IFEM equations are solved utilizing a new variant of the iterative enclosure method. Further, both primary and derived variables are simultaneously solved attaining the same accuracy. As a result, the proposed formulation gives the tightest guaranteed enclosure of the exact solution in comparison with other known interval methods, as illustrated in several numerical examples.