Study On Finite Element Model Updating Method And Iterative Technique For Degree Of Freedom Matching

In this dissertation, model updating methods and iterative techniques for degree of freedom matching in the field of finite element model updating are studied.Accurate finite element (FE) models of engineering structures are needed in order to predict their dynamic characteristics. Nowadays, the appearances of high precision aircrafts and spacecrafts, large scale bridges and other new engineering structures impose higher demands on the reliability and accuracy of their FE models. However, a FE model may be inaccurate especially in the case of complex structures due to difficulties in the modeling of joints, boundary conditions and structural damping. So the development of model updating method which has the ability of correcting the numerical values of individual parameters in a FE model using the data obtained from an associated experimental model is necessary. The updated model can describe the dynamic properties of the subject structure more accurately.The traditional eigensensitivity-based approaches have extensive application, however, this kind of model updating methods pay much attention to the updating results and have many disadvantages, for example, they have limited updating parameters, time consuming, especially, the updated parameters that have high sensitivity may not be the ones that have modeling errors. So it is necessary to find a new method which has high calculation efficiency, does not need sensitivity analysis, updates more parameters simultaneously and finds the parameters that have modeling errors indeed. It is found that the cross-model cross-mode (CMCM) method meet the former requirements, however, the updating results are the correction factor of one element, so in the case of a element has more than one parameter that have modeling errors, the CMCM method lose its updating ability. On the other hand,the denominator of the updating formula may equal or close to zero which leads to the emergence of ill-conditioned problems and brings difficulties to model updating process. This paper propose a new model updating method named as improved cross-model cross-mode (ICMCM) method which based on the CMCM method. The new method avoided the disadvantage of CMCM method by changing the process of formula derivation. Moreover, the updating object can be any physical or geometric parameters of one element, which increase the number of the updating parameters. The ICMCM method with damping is obtained by extending the ICMCM method, which enlarges application range of the original method. A new model updating method based on the frequency response function named as cross-model cross-frequency response function (CMCFRF) method is obtained by using the theory of ICMCM method. Updating results show the effectiveness and superiority of ICMCM method and CMCFRF method.In addition, using the traditional iterative method that associating the model updating method with the degree of freedom matching technique, the errors resulted from replacing the reduction/expansion matrix of the experimental model with those of the FE model are not fully considered, which needs more iterations and computing time in the model updating process. In order to reduce the errors produced in the replacement, based on the traditional methods, a new iterative method named as error cyclic iteration method based on model reduction (ECIMR) that associating the model updating method with the model reduction technique and a new iterative method named as error cyclic iteration method based on modal expansion (ECIME) that associating the model updating method with the modal expansion technique are proposed, in which the correction term related to the errors is added. The convergence rate and the computing time of the new method are significantly superior to those of the traditional iterative method. Because ECIMR method does not limit the model updating method and the model reduction method and ECIME method does not limit the model updating method, both of these two new iteration methods have generalities. One of important advantages of the new iterative methods is that they make the calculation converge with less iteration and computing time than those of the traditional methods, which are very useful for model updating of large-scale engineering structures, they can save much computing time and improve work efficiency. In addition, the model updating precision becomes higher with the precision of the model reduction upgraded after using ECIMR method.In order to further verify the updating ability of the proposed model updating method for the complex structures especially the aerospace structures, GARTEUT model which is the benchmark model for model updating and a cabin structure of a certain type rocket are used as the updating objects, and the perfect updating results are obtained. Updating results show that the modal expansion technique is more suitable for ICMCM method. The ICMCM method using modal expansion can update far more updating parameters than using model reduction, and the updating results are better by using modal expansion than by using model reduction. ICMCM method can update more parameters than the eigensensitivity-based approaches, which can include the parameters with modeling errors as much as possible. The updating equations can automatically update the parameters that have modeling errors indeed and the updating results meet the real physical meaning of the structures using ICMCM method.