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A solution procedure for constrained eigenvalue problems and its application within the structural finite-element code NOSA-ITACA

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Abstract

The paper presents an efficient and reliable implementation of numerical methods for constrained generalized eigenvalue problems, specialized for the modal analysis of linear elastic structures in a finite-element setting. The implementation, which takes into account the sparsity of the stiffness and mass matrices and the features of master-slave constraints, is based on open-source packages embedded in the finite-element code NOSA-ITACA. Numerical tests on historical building are performed, with the aims of calculating their vibration frequencies and mode shape vectors, comparing them to the results of a general purpose commercial code and assessing the accuracy of the tool developed.

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Acknowledgments

The authors are grateful to the referees for constructive comments that significantly improved the presentation. This research was supported by the Region of Tuscany (Project “Tools for modelling and assessing the structural behaviour of ancient constructions: the NOSA-ITACA code”, PAR-FAS 2007-2013). Moreover, the work of the first author was supported by National Group of Computing Science (GNCS-INDAM) (GNCS 2013 Project “Strategie risolutive per sistemi lineari tipo KKT con uso di informazioni strutturali”, GNCS 2013-2014 Project “Identificazione automatica dei parametri algoritmici ottimali”).

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40127 , Bologna, Italy

    Margherita Porcelli

  2. Istituto di Scienza e Tecnologie dell’Informazione Alessandro Faedo, ISTI-CNR, Via G. Moruzzi 1, 56124 , Pisa, Italy

    Margherita Porcelli, Vincenzo Binante, Maria Girardi, Cristina Padovani & Giuseppe Pasquinelli

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  1. Margherita Porcelli
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  2. Vincenzo Binante
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  3. Maria Girardi
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  4. Cristina Padovani
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  5. Giuseppe Pasquinelli
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Correspondence to Margherita Porcelli.

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Porcelli, M., Binante, V., Girardi, M. et al. A solution procedure for constrained eigenvalue problems and its application within the structural finite-element code NOSA-ITACA. Calcolo 52, 167–186 (2015). https://doi.org/10.1007/s10092-014-0112-1

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