Interval Finite Element Analysis of Structural Dynamic Problems

• Published in: SAE International journal of materials and manufacturing Vol. 8; no. 2; pp. 382 - 389
• Main Authors: Xiao, Naijia, Muhanna, Rafi L., Fedele, Francesco, Mullen, Robert L.
• Format: Journal Article
• Language: English
• Published: Warrendale SAE International 14-04-2015; SAE International, a Pennsylvania Not-for Profit
• Subjects: Damping; Dynamic structural analysis; Enclosures; Finite element method; Frequency analysis; Frequency response; Interval; Iterative methods; Material properties; Mathematical intervals; Mathematical vectors; Matrices; Musical intervals; Rectangular plates; Scalars; Stiffness; Uncertainty
• ISSN: 1946-3979; 1946-3987; 1946-3987
• 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.