Abstract
In the present chapter the theoretical basis of different methods developed for the calibration of FEMs are discussed. In general, Model Updating techniques are based on the use of appropriate functions that iteratively update selected physical properties (characteristics of the materials, stiffness of a link, etc.). In this way the correlation between the simulated response and the target value could improve if compared to an initial value. The FE model thus obtained can be used for a detailed structural analysis with a great confidence. The technique described in the first part of the chapter is applied to the evaluation of the structural properties of the tower of the Provincial Administration Building in Bari (Italy).The final purpose is to predict the performance of the tower to different combinations of static and dynamic loads, i.e. earthquakes or other induced vibrations. Ambient vibration tests have been performed on the above mentioned tower with the aim of determining its dynamic response and developing a procedure for modeling this building (Foti et al., 2012a). The Operation Modal Analysis (OMA) has been carried out both in the frequency domain and in the time domain to extract the dominant frequencies and mode shapes of the tower.
TopIntroduction
The use of Finite Element Models (FEMs) for modelling and simulating in detail the behavior of buildings is becoming a popular and useful means for defining the structural and dynamical behavior of civil buildings (Mottershead et al., 1993; Brownjohn et al., 2000; Brownjohn et al., 2003; Ceravolo, 2008; Atamturktur et al., 2010; Betti et al. 2011; Oliveira et al., 2012; Castellano et al., 2015; Diaferio, 2015; Zarate & Caicedo, 2008; Zhang et al., 2000). The always bigger calculus power of the modern processors makes easy the realization of FEMs with a very big number of elements. As a consequence it is easier to simulate also complicate structures with an high level of accuracy. The main problem is related to the difficulty of tuning the model to the real building, especially in the evaluation of geometrical data and materials’ properties. For this reason, modern techniques for correctly tuning the model have been recently introduced. The most interesting methods are based on experimental data obtained with non-destructive tests. The latter is a necessary condition especially when the analysis is carried out on historical and important buildings (Bayraktar et al. 2009; Brownjohn et al., 2000, 2003; Carnimeo et al., 2015; Chang et al., 2001; D’Ambrisi et al. 2012; Debnath et al., 2012; Diaferio et al., 2007, 2010, 2014a, 2014c, 2014e, 2015; Feng et al., 1998; Florin & Sunai, 2010; Foti, 2013, 2014; Foti et al., 2011, 2012b, 2014, 2015; Gentile & Saisi, 2007, 2013; Ivorra & Palleres, 2006; Julio et al., 2008; Jaishi et al., 2005; Lepidi et al., 2009; Lourenço, 2002; Magalhaes et al. 2008, 2010; Oliveira et al., 2012; Osmancikli et al., 2012; Pagnotta, 2008; Sevim et al., 2011; Tomaszewska et al., 2012; Vincenzi, 2007;).
Key Terms in this Chapter
Finite Element Method: Is a numerical analysis technique used to model a wide variety of physical problems. The method starts discretizating the structure into a series of elements connected at specific nodes. The method requires that the solution is continuous along common boundaries of adjacent elements.
Modal Assurance Criterion (MAC) Index: Is to provide a measure of consistency (degree of linearity) between estimates of a modal vector and so it is an effective criterion for performing the comparison and quantify the correspondence between two sets of mode shapes.
Model Updating: Is a process with the main aim of match the response of a numerical model to the experimental data.
Operational Modal Analysis (OMA): Is a procedure for the identification of the modal properties of a structure. The technique makes use of the vibration data collected when the structure is under its operating conditions.
Sensitivity analysis: Is the basis of Finite Element model calibration methods that search the solution using a first order Taylor’s series development that minimizes the error function between the model and experimental data consequently to a modification of the model parameters.
Dynamic Tests: Are tests performed on structures subjected to dynamic loads. During the test the structural response is recorded in chosen point by means of sensors.