Abstract
This paper deals with the problem of updating simultaneously mass and stiffness matrices. The desired matrix properties, including satisfaction of the characteristic equation, symmetry, positive semidefiniteness, and boundedness, are imposed as side constraints to form the matrix pencil minimization problem. This problem is related to finite element model updating and damage detection of a structure. Using partial Lagrangian multipliers, we convert the matrix pencil minimization problem into a monotone matrix linear variational inequality, and develop the projection and contraction method. Based on the special structure of the matrix linear variational inequality, we derive an efficient implementation of the projection and contraction method for large-scale problems. Several numerical tests are presented to illustrate the performance and application of the proposed method.
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