Por lo tanto, puede concluirse que el método propuesto se considera una opción útil y e…ciente para el análisis paramétrico de modi…caciones locales en grandes estructuras.ii ABSTRACT When developing structural design and analysis some projects require dynamic analysis of large …nite element models with millions of degrees of freedom which use large size data …les.The analysis complexity and size grow if a parametric analysis is required. This problem has been approached traditionally in several ways: one way is increasing the power and the storage capacity of computer systems involved in the analysis. Other obvious way is reducing the total amount of analyses and their details. Finally, complementary methods to …nite element analysis can also be employed in order to limit the number of variables and to reduce the execution time keeping the results as close as possible to the actual behaviour of the structure.Following this third option, we propose a model reduction method that is based in a simpli…ed analysis that supplies a solution for the dynamic response of the structure in the complex modal space using few data. Thereby, parametric analysis can be done varying multiple parameters so as to obtain a solution which complies with the desired objetive. We propose not only mass, sti¤ness and damping variations, but also addition of degrees of freedom to the original structure in order to calculate the transient and steady-state response. Additionally, the simple implementation of the procedure allows an in-depth control of the problem variables.Furthermore, improvements such as di¤erent ways to obtain eigenvectors or to remove damping limitations of the original structure are also possible.The purpose of the procedure is similar to that of using the Guyan or similar model order reduction techniques. However, in our method we do not perform a true model order reduction in the traditional sense. Furthermore, additional gains, which we do not explore herein, can be obtained through the combination of this method with traditional model-order reduction procedures. In our procedure we use the information of the whole system of equations is used but only those nodes of interest to the analyst are processed. That interest comes from the need to obtain the response of the structure at speci…c locations or from the need to modify the structure at some suitable positions in order to change its behaviour (acceleration, velocity or displacement response) under dynamic loads. Therefore, the procedure is particularly suitable for parametric optimization in large structures with >100000 normal modes such as position of new elements, sti¤ness, mass and viscous dampings in previous studies where di¤erent solutions are devised and optimized, and in the case of large structures, can carry an extremely high iii
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