Substructuring approache in state space models for dynamic system parameters identification

In the recent decade, the request for structural health monitoring expertise increased exponentially in the United States. The aging issues that most of the transportation structures are experiencing can put in serious jeopardy the economic system of a region as well as of a country. At the same time, the monitoring of structures is a central topic of discussion in Europe, where the preservation of historical buildings has been addressed over the last four centuries. More recently, various concerns arose about security performance of civil structures after tragic events such the 9/11 or the 2011 Japan earthquake: engineers looks for a design able to resist exceptional loadings due to earthquakes, hurricanes and terrorist attacks. After events of such a kind, the assessment of the remaining life of the structure is at least as important as the initial performance design. Consequently, it appears very clear that the introduction of reliable and accessible damage assessment techniques is crucial for the localization of issues and for a correct and immediate rehabilitation. The System Identification is a branch of the more general Control Theory. In Civil Engineering, this field addresses the techniques needed to find mechanical characteristics as the stiffness or the mass starting from the signals captured by sensors. The objective of the Dynamic Structural Identification (DSI) is to define, starting from experimental measurements, the modal fundamental parameters of a generic structure in order to characterize, via a mathematical model, the dynamic behavior. The knowledge of these parameters is helpful in the Model Updating procedure, that permits to define corrected theoretical models through experimental validation. The main aim of this technique is to minimize the differences between the theoretical model results and in situ measurements of dynamic data. Therefore, the new model becomes a very effective control practice when it comes to rehabilitation of structures or damage assessment. The instrumentation of a whole structure is an unfeasible procedure sometimes because of the high cost involved or, sometimes, because it’s not possible to physically reach each point of the structure. Therefore, numerous scholars have been trying to address this problem. In general two are the main involved methods. Since the limited number of sensors, in a first case, it’s possible to gather time histories only for some locations, then to move the instruments to another location and replay the procedure. Otherwise, if the number of sensors is enough and the structure does not present a complicate geometry, it’s usually sufficient to detect only the principal first modes. This two problems are well presented in the works of Balsamo [1] for the application to a simple system and Jun [2] for the analysis of system with a limited number of sensors. Once the system identification has been carried, it is possible to access the actual system characteristics. A frequent practice is to create an updated FEM model and assess whether the structure fulfills or not the requested functions. Once again the objective of this work is to present a general methodology to analyze big structure using a limited number of instrumentation and at the same time, obtaining the most information about an identified structure without recalling methodologies of difficult interpretation. A general framework of the state space identification procedure via OKID/ERA algorithm is developed and implemented in Matlab. Then, some simple examples are proposed to highlight the principal characteristics and advantage of this methodology. A new algebraic manipulation for a prolific use of substructuring results is developed and implemented.

Investigation on laser shock peening capability by FE simulation

Laser shock peening is a technique similar to shot peening that imparts compressive residual stresses in materials for improving fatigue resistance. The ability to use a high energy laser pulse to generate shock waves, inducing a compressive residual stress field in metallic materials, has applications in multiple fields such as turbo-machinery, airframe structures, and medical appliances. The transient nature of the LSP phenomenon and the high rate of the laser's dynamic make real time in-situ measurement of laser/material interaction very challenging. For this reason and for the high cost of the experimental tests, reliable analytical methods for predicting detailed effects of LSP are needed to understand the potential of the process. Aim of this work has been the prediction of residual stress field after Laser Peening process by means of Finite Element Modeling. The work has been carried out in the Stress Methods department of Airbus Operations GmbH (Hamburg) and it includes investigation on compressive residual stresses induced by Laser Shock Peening, study on mesh sensitivity, optimization and tuning of the model by using physical and numerical parameters, validation of the model by comparing it with experimental results. The model has been realized with Abaqus/Explicit commercial software starting from considerations done on previous works. FE analyses are “Mesh Sensitive”: by increasing the number of elements and by decreasing their size, the software is able to probe even the details of the real phenomenon. However, these details, could be only an amplification of real phenomenon. For this reason it was necessary to optimize the mesh elements' size and number. A new model has been created with a more fine mesh in the trough thickness direction because it is the most involved in the process deformations. This increment of the global number of elements has been paid with an "in plane" size reduction of the elements far from the peened area in order to avoid too high computational costs. Efficiency and stability of the analyses has been improved by using bulk viscosity coefficients, a merely numerical parameter available in Abaqus/Explicit. A plastic rate sensitivity study has been also carried out and a new set of Johnson Cook's model coefficient has been chosen. These investigations led to a more controllable and reliable model, valid even for more complex geometries. Moreover the study about the material properties highlighted a gap of the model about the simulation of the surface conditions. Modeling of the ablative layer employed during the real process has been used to fill this gap. In the real process ablative layer is a super thin sheet of pure aluminum stuck on the masterpiece. In the simulation it has been simply reproduced as a 100µm layer made by a material with a yield point of 10MPa. All those new settings has been applied to a set of analyses made with different geometry models to verify the robustness of the model. The calibration of the model with the experimental results was based on stress and displacement measurements carried out on the surface and in depth as well. The good correlation between the simulation and experimental tests results proved this model to be reliable.

Updating of Finite Element Models using static and dynamic optical strains with application to damage assessment

In the recent years, vibration-based structural damage identification has been subject of significant research in structural engineering. The basic idea of vibration-based methods is that damage induces mechanical properties changes that cause anomalies in the dynamic response of the structure, which measures allow to localize damage and its extension. Vibration measured data, such as frequencies and mode shapes, can be used in the Finite Element Model Updating in order to adjust structural parameters sensible at damage (e.g. Young’s Modulus). The novel aspect of this thesis is the introduction into the objective function of accurate measures of strains mode shapes, evaluated through FBG sensors. After a review of the relevant literature, the case of study, i.e. an irregular prestressed concrete beam destined for roofing of industrial structures, will be presented. The mathematical model was built through FE models, studying static and dynamic behaviour of the element. Another analytical model was developed, based on the ‘Ritz method’, in order to investigate the possible interaction between the RC beam and the steel supporting table used for testing. Experimental data, recorded through the contemporary use of different measurement techniques (optical fibers, accelerometers, LVDTs) were compared whit theoretical data, allowing to detect the best model, for which have been outlined the settings for the updating procedure.