| Author: | Tian, Wei |
| Title: | Substructuring methods for responses, response sensitivity, and model updating of nonlinear systems |
| Advisors: | Xia, Yong (CEE) |
| Degree: | Ph.D. |
| Year: | 2023 |
| Subject: | Structural analysis (Engineering) Structural dynamics Hong Kong Polytechnic University -- Dissertations |
| Department: | Department of Civil and Environmental Engineering |
| Pages: | xviii, 181 pages : color illustrations |
| Language: | English |
| Abstract: | Civil engineering structures exhibit nonlinearities. Finite element model updating of these structures is significant to obtain a more accurate numerical model for various applications, such as damage detection, response prediction, and vibration control. Model updating of a nonlinear system usually requires the structural responses and response sensitivities with respect to all updating parameters to be calculated iteratively within each time step, which consumes considerable computational time and memory. The substructuring method has been proven to be very effective in reducing computational loads for linear systems. This PhD study develops two substructuring methods to calculate the structural responses, response sensitivities, and model updating for structures with material nonlinearities and geometric nonlinearities. In the first part, a substructuring method is developed for systems with localized material nonlinearities. The nonlinearity is first detected and located using the ordinary coherence function. The global structure is then divided into linear and nonlinear substructures. After division, the nonlinearities are localized within a few nonlinear substructures only. The responses of the linear substructures are interpreted as the combination of a few master modal responses based on the mode superposition. The contribution of the discarded slave modal responses is compensated by responses of the nonlinear substructures and master modal responses and external excitation of the linear substructures via transformation matrices, based on which the global system is projected into a reduced one. The structural responses and response sensitivities are then solved based on the reduced system. The precision and efficiency of the proposed method are verified by a nonlinear spring-mass system and a large-scale nonlinear frame. Next, the substructuring method is developed for sensitivity-based nonlinear model updating. The analytical responses and response sensitivities with respect to the design parameters are calculated efficiently by the substructuring method to form the objective function and Jacobian matrix in model updating. The elemental parameters in the linear and nonlinear substructures are then adjusted simultaneously so that the analytical responses match the measured ones in an optimal manner. Only the concerned substructures and the reduced equation are re-analyzed in the optimization process, thus reducing the computational load significantly compared with the traditional method performed on the global structure. The application to a nine-story frame with nonlinear base isolations demonstrates that the proposed method is very accurate and efficient in updating the linear and nonlinear parameters simultaneously with a few measured responses. The effects of measurement noise and the number of measurement points on the updating results are also investigated. The final part of the thesis is to develop a modal derivative enhanced substructuring method for the systems with geometric nonlinearities. The method approximates the substructural displacements by a quadratic modal manifold around the initial linear equilibrium position, which is governed by a few substructural master modes only. A time-variant reduction basis augmented by the modal derivatives of the master modes is derived from the quadratic modal manifold, which enables the geometric nonlinearities to be accurately captured. By using the reduction basis, the global system is transformed into a reduced one containing the master modes only. The master modal responses and response sensitivities are solved efficiently from the reduced system. The global structural responses and response sensitivities are recovered from the master modal solutions based on the quadratic modal manifold. The accuracy of the proposed method is finally validated by a thin plate structure. |
| Rights: | All rights reserved |
| Access: | open access |
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