Proximal-point method for finite element model updating problem

The problem of finding the optimal approximation to analytical stiffness matrix modeled by the finite element method is considered in this paper. Desired matrix properties, including satisfaction of the dynamic equation, symmetry, positive semidefiniteness and physical connectivity, are imposed as side constraints of the minimization problem. To the best of the author's knowledge, the finite element model updating problem containing all these constraints simultaneously has not been proposed in the literature earlier. By partial Lagrangian multipliers technique, the optimization problem is transformed into a matrix linear variational inequality and the proximal-point method is first used to solve the equivalent problem. The results of numerical examples show that the proposed method works well even for incomplete measured data.

► The finite element model updating problem containing all necessary constraints is considered.
► The proximal point method is first used to update the finite element model.
► The numerical examples show that our method works well for incomplete measured data.