Finite element model updating in structural dynamics using design sensitivity and optimisation
Model updating is an important issue in engineering. In fact a well-correlated model provides for accurate evaluation of the structure loads and responses. The main objectives of the study were to exploit available optimisation programs to create an error localisation and updating procedure of nite element models that minimises the "error" between experimental and analytical modal data, addressing in particular the updating of large scale nite element models with severe requirements on the mode shapes correlation. A new methodology and procedure that allows the semi-automatic adjustment of a large nite element dynamic model of a structure to better represent the dynamic characteristics of an actual structure was developed. The key aspect of the procedure is a "two steps" optimisation process to achieve a complete correlation of the modal data. Eigenfrequency deviations and mode shapes cross-othogonality (CO) and/or modal assurance criterion (MAC) are used in the objective functions for the estimation problem of the updating parameters, that are the variables for tuning the analytical model. Theoretical aspects and practical implementation conceming CO and MAC, and their derivatives, have been fully developed and the advantages of using these mode correlation indices in the objective function have been largely commented. The selection of the updating parameters is a complex issue and can be still considered a partially open point. In the new procedure the suggested automated selection of the updating parameters by means of a preliminary calculation of the element modal strain energy and eigenvalue sensitivities is adequate for the reduction of the frequency deviations but could not be to improve the correlation indices of the mode shapes. The new procedure was successfully applied four times: to a cantilever beam model, the Garteur model, the Spacehab dynamic model and the Mini-Pressurised Logistics Module model. The last application was a real life application on a large scale structural mathematical model and in this case the procedure was mainly used for error localisation purposes. The developed procedure is robust, effective and efficient, thus the original objectives of the study were largely met.