| dc.description.abstract | The problem of structural modification and reanalysis plays a key role in the structure analysis, redesign and optimization of a structural system. Based on the previous researches, the present thesis tends to investigate deeply the methods of structural modification and dynamic reanalysis to increase the accuracy and computational efficiency under the same convergent criterion.
As the advance of technology, the request for the characteristics and qualification of engineering structure becomes higher and higher. Many complex factors must be taken into consideration during the design stage, and it results in the increase of freedom in the structural dynamic model. The conventional, one-time computational analysis for the dynamic characteristics is highly consumed in time, cost, and man-power, and may not be workable sometime. The structural modification and reanalysis aims to reduce the computational cost. To reduce the computational cost, a complete analysis of the modified structure is avoided in the redesign and reanalysis stage. Based on the previous researches, the dynamic information of the original structure can be used as the basis of the reanalysis. A proper analytical method, plus accurate dynamic information of the original structure, will largely affect the results of reanalysis.
The present thesis analyzes the structural dynamic characteristics by the matrix-based Chebyshev spectral method, or so called differentiation matrix method. A m-file of matrix characteristic value in Matlab is then adopted to analyze the model parameters of the structure subjected to different boundary conditions. The structure reanalysis is then preceded based on the initial structural information.
To assure accurate solutions, algebraic method is used to investigate the modified structural, re-analysis problem, equal inertia transformation is then used to find out the implicit roots of the dynamic, stiffness matrix. A computational method is derived to find out the eigenvalues. Based on the known implicit roots, the characteristics and solutions of the implicit vectors are investigated. The present thesis illustrates several approximate methods and compares the corresponding accuracy. A combined approximation method based on the reduced basis is then used as the best tool of reanalysis. The present thesis investigates the theoretical ground of reduced basis, and then derives the solutions by combined approximate method for static structural system, as well as dynamic structural system. Results show that the combined approximate can effectively and accurately find out the approximate solutions for a minor modified structure, even for a major modified structure.
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