Abstract
An exact approach is proposed for damage identification in statically determinate structures. The contribution of this study is twofold. Firstly, a rigorous disassembly formulation of structural global flexibility matrix is presented based on the matrix spectral decomposition, which can provide an exact relationship between the modifications of structural stiffness parameters and the associated flexibility matrix. Secondly, the static minimum-rank flexibility change is derived to obtain the exact flexibility change before and after damage. The proposed method is economical in computation and is simple to implement. For the statically determinate structures, the proposed method can exactly compute the elemental perturbed stiffness parameter only using a few of incomplete static displacement data. The efficiency of the proposed method is demonstrated by two statically determinate structures.
Highlights
Detection, localization, and quantification of damage in a structure via techniques that examine changes in measured structural static/dynamic response have attracted much attention in recent years
A rigorous disassembly formulation of structural global flexibility matrix is presented based on the matrix spectral decomposition, which can provide an exact relationship between the modifications of structural stiffness parameters and the associated flexibility matrix
It has been shown that the proposed method is applicable when the flexibility is estimated in an approximate way by using modal parameters
Summary
Localization, and quantification of damage in a structure via techniques that examine changes in measured structural static/dynamic response have attracted much attention in recent years. One important group of damage identification methods is the perturbation-based techniques [13–35] These methods start with the derivatives of the response parameters to changes in material and physical parameters. It is anticipated that the computational cost of these existing sensitivity methods will be very expensive for large damage case, since a higher-order approximation should be performed or an iteration scheme must be used to estimate the perturbation parameters more precisely. A rigorous disassembly formulation of structural global flexibility matrix is presented based on the matrix spectral decomposition, which can provide an exact relationship between the modifications of structural stiffness parameters and the associated flexibility matrix. Mathematical Problems in Engineering compute the elemental perturbed stiffness parameter only using a few of incomplete static displacements without any higher-order approximation or iteration. In the following theoretical development, it is assumed that structural damages only reduce the system stiffness matrix and structural refined FEM has been developed before damage occurrence
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