Matrix linear variational inequality approach for finite element model updating

The problem of finding the least change adjustment to analytical stiffness matrix modeled by finite element method is considered in this paper. Desired matrix properties, including satisfaction of the dynamic equation, symmetry, positive semidefiniteness and sparse pattern, are imposed as side constraints of the nonlinear optimization problem. To the best of the author's knowledge, the matrix updating problem containing all these constraints simultaneously has not been proposed in the literature earlier. By partial Lagrangian multipliers technique, the optimization problem is first reformulated as an equivalent matrix linear variational inequality (MLVI) and solved by extended projection and contraction method. The results of numerical examples show that the proposed method works well even for incomplete measured data.

► All necessary conditions of the finite element model are imposed as constraints.
► Specially, the finite element model takes structure connectivity into consideration.
► Finite element model updating problem is first reformulated as MLVI.
► Extended projection and contraction method works well for incomplete measured data.