ANALYSIS OF MECHANICAL SYSTEMS USING INTERVAL COMPUTATIONS APPLIED TO FINITE ELEMENT METHODS

• Published in: Journal of sound and vibration Vol. 239; no. 5; pp. 949 - 968
• Main Authors: DESSOMBZ, O., THOUVEREZ, F., LAÎNÉ, J.-P., JÉZÉQUEL, L.
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 01.02.2001; Elsevier
• Subjects: Beams, plates and shells; Computational techniques; Exact sciences and technology; Finite-element and galerkin methods; Fundamental areas of phenomenology (including applications); Mathematical methods in physics; Physics; Solid mechanics; Structural and continuum mechanics; Structural mechanics (beam, string...); Theory and numerical methods; Finite element method; Linear systems; Uncertain systems; Transfer functions; Physical parameter; Clamped plate; Mechanical system; Convergence rate; Systems analysis; Numerical method; Iterative methods; Beam(mechanics)
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1006/jsvi.2000.3191

This paper addresses the problem of mechanical systems in which parameters are uncertain and bounded. Interval calculation is used to find an envelope of transfer functions for mechanical systems modelled with finite elements. Within this context, a new formulation has been developed for finite element problems involving bounded parameters, to avoid the problems of overestimation. An iterative algorithm is introduced, which leads to a conservative solution for linear mechanical problems. A method to ensure the convergence of this algorithm is also proposed. This new algorithm has been tested on simple mechanical systems, and leads to a conservative envelope of the transfer functions.