|Title:||A new substructuring method for model updating of large-scale structures|
|Subject:||Hong Kong Polytechnic University -- Dissertations|
Structural analysis (Engineering)
Finite element method
|Department:||Department of Civil and Structural Engineering|
|Pages:||xxi, 293 p. : ill. (some col.) ; 30 cm.|
|Abstract:||In vibration-based model updating, the finite element model is iteratively modified to ensure its vibration properties reproduce the measured counterparts in an optimal way. The finite element model of a large-scale structure usually consists of a large number of degrees of freedom. Calculating the eigensolutions and eigensensitivities of such a finite element model and updating it are very expensive in terms of computation time and memory. The substructuring method is a promising solution for reducing computation load in both of these tasks. This PhD study develops a forward and an inverse substructuring approaches that can be used to update finite element models of large-scale structures. In the forward substructuring approach, the eigensolutions and eigensensitivities of the global structure are calculated from those of the independent substructures and compared with global structure measurements through an optimization process. Kron's substructuring method for eigensolutions is improved in terms of computational efficiency by retaining only the first few eigenmodes of the independent substructures as master modes to assemble a reduced eigenequation for the global structure. This improvement not only reduces the computational endeavor required in extracting the complete eigenmodes of all the substructures, but also produces a smaller eigenequation that is frequently analyzed during the model updating process. The reduced eigenequation for eigensolutions is subsequently extended to calculate the first-order and high-order eigensensitivities of the global structure with respect to elemental parameters. The eigensensitivity matrices are determined from the derivative matrices of only those substructures that contain the designed elements, thus realizing a significant reduction in computational cost. In consequence, the calculated eigensolutions and eigensensitivities are used in the practical model updating process. As accurate eigensolutions and eigensensitivities are needed in the final steps of the model updating procedure, an iterative scheme is proposed to calculate the eigensolutions and eigensensitivities more accurately using only a few master modes.|
In the second part of the thesis, an inverse substructuring approach is developed by extracting substructural flexibility matrices from the experimental modal data. As a result, the focused substructure is treated as an independent structure to be updated directly using a global model updating method, thus accelerating the conventional optimization process significantly. The model condensation technique is also employed, as the measurement exercise is usually conducted at an incomplete set of points on a practical structure. This inverse substructuring approach allows for the focused substructures to be updated directly based purely on the measurements taken in the local area. The proposed substructuring-based model updating approaches are applied to a few numerical, laboratory, and real structures. The results verify that these substructuring methods are computationally efficient and accurate in finite element model updating and associated applications.
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