Finite element model updating with positive definiteness and no spill-over

Updating a finite element model to match measured spectral information has been a important task for engineers. In the process, it is desirable to match only the measured spectral information without tampering with the other unmeasured and unknown eigeninformation in the original model and to maintain positive definiteness (semidefiniteness) in the coefficient matrices. In this paper, we present a new direct method for the finite element model updating. By constructing a parametric symmetric low-rank correction form, the method can preserve both no spill-over and positive definiteness (semidefiniteness) of the mass and stiffness matrices. Using the parametric form, necessary and sufficient conditions under which this problem is solvable are obtained and a minimum modification is given explicitly. Numerical examples show that the method is efficient.

► We present a model updating method with positive definiteness and no spill-over.
► A parametric symmetric low-rank correction form is constructed.
► Necessary and sufficient conditions for solvability of the correction are obtained.
► The minimum modification solution is given explicitly.