Xiao, N., Muhanna, R., Fedele, F., and Mullen, R., "Interval Finite Element Analysis of Structural Dynamic Problems," SAE Int. J. Mater. Manf. 8(2):382-389, 2015, doi:10.4271/2015-01-0484.
We analyze the frequency response of structural dynamic systems with uncertainties in load and material properties. We introduce uncertainties in the system as interval numbers, and use Interval Finite Element Method (IFEM). Overestimation due to dependency is reduced using a new decomposition for the stiffness and mass matrices, as well as for the nodal equivalent load. In addition, primary and derived quantities are simultaneously obtained by means of Lagrangian multipliers that are introduced in the total energy of the system. The obtained interval equations are solved by means of a new variant of the iterative enclosure method resulting in guaranteed enclosures of relevant quantities. Several numerical examples show the accuracy and efficiency of the new formulation.