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2019
Journal article
Open Access

**Finite element model updating for structural applications**

*Girardi M., Padovani C., Pellegrini D., Porcelli M., Robol L.*

A novel method for performing model updating on finite element models is presented. The approach is particularly tailored to modal analyses of buildings, by which the lowest frequencies, obtained by using sensors and system identification approaches, need to be matched to the numerical ones predicted by the model. This is done by optimizing some unknown material parameters (such as mass density and Young's modulus) of the materials and/or the boundary conditions, which are often known only approximately. In particular, this is the case when considering historical buildings.
The straightforward application of a general-purpose optimizer can be impractical, given the large size of the model involved. In the paper, we show that, by slightly modifying the projection scheme used to compute the eigenvalues at the lowest end of the spectrum one can obtain local parametric reduced order models that, embedded in a trust-region scheme, form the basis for a reliable and efficient specialized algorithm.
We describe an optimization strategy based on this approach, and we provide numerical experiments that confirm its effectiveness and accuracy.**Source: **Journal of computational and applied mathematics 370 (2019). doi:10.1016/j.cam.2019.112675**DOI: **10.1016/j.cam.2019.112675

**See at: **
Journal of Computational and Applied Mathematics | ISTI Repository | Journal of Computational and Applied Mathematics | Journal of Computational and Applied Mathematics | Journal of Computational and Applied Mathematics | Journal of Computational and Applied Mathematics | Journal of Computational and Applied Mathematics | CNR ExploRA | Journal of Computational and Applied Mathematics | Journal of Computational and Applied Mathematics | www.sciencedirect.com

2018
Conference article
Open Access

**Fea for masonry structures and vibration-based model updating using NOSA-ITACA**

*Girardi M., Padovani C., Pellegrini D., Porcelli M., Robol L.*

NOSA-ITACA is a finite-element code developed by the Mechanics of Materials and Structures Laboratory of ISTI-CNR for the structural analysis of masonry constructions of historical interest via the constitutive equation of masonry-like materials. The latest improvements in the software allow applying model updating techniques to match experimentally measured frequencies in order to fine-tune calculation of the free parameters in the model. The numerical method is briefly presented and applied to two historical buildings in Lucca, the Church of San Francesco and the Clock Tower.**Source: **10th International Masonry Conference, pp. 723–735, Milano, Italy, 9-11 July 2018

**See at: **
ISTI Repository | CNR ExploRA

2017
Software
Open Access

**NOSA-ITACA 1.1**

*Binante V., Girardi M., Padovani C., Pasquinelli G., Pellegrini D., Porcelli M., Robol L.*

NOSA-ITACA is a code for the nonlinear structural analysis of historical masonry constructions. It the result of the integration of the finite element code NOSA into the open-source SALOME platform.

**See at: **
ISTI Repository | CNR ExploRA | www.nosaitaca.it

2016
Conference article
Open Access

**Safety assessment of masonry constructions via numerical tools: the NOSA-ITACA code**

*Binante V., Girardi M., Lucchesi M., Padovani C., Pellegrini D., Margherita P.*

This paper describes the main features of the NOSA-ITACA code, software for the structural analysis of masonry buildings of historical interest resulting from integration of the finite element code NOSA and the open-source platform SALOME. After a short description of the constitutive equation used to model the mechanical behaviour of masonry constructions, some details are given concerning the code's implementation. Then, the result of a static analysis of the "Voltone" in Livorno, performed via the NOSAITACA code, is presented with the aim of highlighting the important role of mathematical models and numerical tools in assessing the safety of historical masonry buildings.**Source: **18th ICOMOS General Assembly and Symposium: "Heritage and Landscape as Human Values", pp. 418–424, Florence, Italy, 9-14 November 2014

**See at: **
ISTI Repository | CNR ExploRA

2014
Software
Open Access

**NOSA-ITACA**

*Binante V., Girardi M., Padovani C., Pasquinelli G., Pellegrini D., Porcelli M.*

NOSA-ITACA is a code for the nonlinear structural analysis of historical masonry constructions. It the result of the integration of the finite element code NOSA into the open-source SALOME platform.

**See at: **
ISTI Repository | CNR ExploRA | www.nosaitaca.it

2014
Journal article
Restricted

**New updates of incomplete LU factorizations and applications to large nonlinear systems**

*Bellavia S., Morini B., Porcelli M.*

In this paper, we address the problem of preconditioning sequences of large sparse indefinite systems of linear equations and present two new strategies to construct approximate updates of factorized preconditioners. Both updates are based on the availability of an incomplete factorization for one matrix of the sequence and differ in the approximation of the so-called ideal update. For a general treatment, an incomplete LU (ILU) factorization is considered, but the proposed approaches apply to incomplete factorizations of symmetric matrices as well. The first strategy is an approximate diagonal update of the ILU factorization; the second strategy relies on banded approximations of the factors in the ideal update. The efficiency and reliability of the proposed preconditioners are shown in the solution of nonlinear systems of equations by preconditioned Newton-Krylov methods. Nearly matrix-free implementations of the updating strategy are provided, and numerical experiments are carried out on application problems.**Source: **Optimization methods & software (Print) 29 (2014): 321–340. doi:10.1080/10556788.2012.762517**DOI: **10.1080/10556788.2012.762517

**See at: **
Optimization Methods and Software | Optimization Methods and Software | Archivio istituzionale della ricerca - Alma Mater Studiorum Università di Bologna | CNR ExploRA | Optimization Methods and Software | Optimization Methods and Software | www.tandfonline.com | Optimization Methods and Software

2013
Report
Closed Access

**A variable fixing version of the two-block nonlinear constrained Gauss-Seidel algorithm for l1-regularized least-squares**

*Porcelli M., Rinaldi F.*

The problem of finding sparse solutions to underdetermined systems of linear equations is very common in many fields like e.g. signal/image processing and statistics. A standard tool for dealing with sparse recovery is the l1-regularized least-squares approach that has been recently attracting the attention of many researchers. In this paper, we describe a new version of the two-block nonlinear constrained Gauss- Seidel algorithm for solving l1-regularized least-squares that at each step of the iteration process fixes some variables to zero according to a simple rule. We prove the global convergence of the method and we report numerical results on some test problems showing the efficiency of the implemented algorithm.**Source: **ISTI Technical reports, 2013

**See at: **
CNR ExploRA

2013
Report
Open Access

**Aircraft fuselage sizing with multilevel optimization**

*Colson B., Porcelli M., Toint P.*

In this technical report we describe the activity research carried out in the years 2010-2012 at Department of Mathematics, University of Namur, Namur (Belgium) in collaboration with LMS Samtech, Angleur (Belgium), in the framework of the project "Méthodes de résolution de problèmes d'optimisation de grande taille pour les structures en matériaux composites" (Acronym LARGO "LARge-scale Optimization problems"). LARGO was granted by the Walloon Region and LMS Samtech in the context of the First Program (convention number 916981).**Source: **ISTI Technical reports, 2013

**See at: **
ISTI Repository | CNR ExploRA

2013
Contribution to conference
Open Access

**On the numerical solution of constrained eigenvalue problems in structural engineering**

*Porcelli M., Binante V., Girardi M., Padovani C., Pasquinelli G., Pellegrini D.*

The poster is devoted to the analysis of the numerical linear algebra issues arising in the modal analysis of structures with application to masonry construction of historical interest. Although the constitutive equation adopted for masonry is nonlinear, modal analysis gives important qualitative information on the dynamic behavior of masonry structures and allows for assessing their seismic vulnerability, while taking Italian regulations into account. Modal analysis consists in the solution of a constrained eigenvalue problem arising from the solution of the free vibration equilibrium equations in a finite-element setting and involves the mass and stiffness matrices and a set of constraints which enforce relationships between degrees of freedom. A simple example of a constraint, is the imposition of the Dirichlet boundary conditions which usually consists in setting certain degrees of freedom to zero (single-point or fixed constraints). A further example is given by the so called master-slave constraints which impose that the displacement of a node (called the slave) depends linearly on the displacements of other nodes (called the masters). These constraints are crucial, e.g., in modeling the contact interaction between masonry and reinforcement. We propose an efficient implementation of numerical methods for constrained eigenvalue problems, specialized for the modal analysis of structures taking into account both the sparsity of the matrices and the features of master-slave constraints. The implementation will be based on open-source packages embedded in the finite-element code NOSA-ITACA developed in the framework of a research project funded by the Region of Tuscany (www.nosaitaca.it/en/). Numerical examples will be shown on the Project case study "Voltone" - a large vaulted masonry structure located beneath Piazza della Repubblica in Livorno, Italy.**Source: **Recent Advances on Optimization, Toulouse, France, 24-26 Luglio 2013

**See at: **
ISTI Repository | CNR ExploRA

2013
Contribution to conference
Open Access

**New preconditioner updates in Newton-Krylov methods for nonlinear systems**

*Porcelli M., Bellavia S., Morini B.*

We address the problem of preconditioning sequences of large sparse indefinite systems of linear equations arising in the solution of large nonlinear systems via Newton-Krylov methods. We present two new strategies to construct approximate updates of a factorized preconditioner for a reference matrix of the sequence. Both updates are based on the availability of an incomplete factorization for one matrix of the sequence and differ in the approximation of the so-called ideal updates. Furthermore, nearly matrix-free implementations are discussed.**Source: **11th EUROPT Workshop on Advances in Continuous Optimization, Firenze, 26-28 Giugno 2013

**See at: **
ISTI Repository | CNR ExploRA

2013
Report
Closed Access

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

*Porcelli M., Binante V., Girardi M., Padovani C., Pasquinelli G.*

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.**Source: **ISTI Technical reports, 2013

**See at: **
CNR ExploRA

2012
Contribution to conference
Open Access

**Progetto NOSA-ITACA - caso studio: il Voltone, piazza della Repubblica, Livorno**

*Binante V., Girardi M., Padovani C., Pasquinelli G., Porcelli M., Pellegrini D., Lucchesi M.*

NOSA-ITACA project, description of the case study**Source: **Salone dell'Arte e del Resaturo di Firenze, Firenze, 8-9-10 Novembre 2012

**See at: **
ISTI Repository | CNR ExploRA

2012
Contribution to conference
Open Access

**Innovative multilevel techniques for structural optimization**

*Porcelli M., Colson B., Toint P. L.*

We address the structural optimization problem of sizing an aircraft fuselage. The problem consists in computing the dimensions of the dierent elements constituting a fuselage mini- mizing the total mass subject to some mechanical constraints. Mathematically, the problem may be formulated as a very large nonlinear optimization problem subjected to several non- linear inequality constraints. We show that this problem possesses a natural hierarchical structure that can be exploited by a multilevel approach. This approach is innovative in the industrial sector and represents a promising alternative to the commonly employed decom- position strategies. Hence, we propose a multilevel procedure which embeds the Recursive Multilevel Trust Region method [1] into an Augmented Lagrangian framework. Some results on both academic and industrial test cases are presented.**Source: **Congresso Biennale SIMAI MiniSimposio: MSP - Large-Scale Numerical Linear Algebra And Optimization, Torino, 25-28 June 2012

**See at: **
ISTI Repository | CNR ExploRA

2012
Contribution to conference
Restricted

**Innovative multilevel techniques for structural optimization.**

*Colson B., Porcelli M., Toint P. L.*

We address the structural optimization problem of sizing an aircraft fuselage. The problem consists in computing the dimensions of the dierent elements constituting a fuselage mini- mizing the total mass subject to some mechanical constraints. Mathematically, the problem may be formulated as a very large nonlinear optimization problem subjected to several non- linear inequality constraints. We show that this problem possesses a natural hierarchical structure that can be exploited by a multilevel approach. This approach is innovative in the industrial sector and represents a promising alternative to the commonly employed decom- position strategies. Hence, we propose a multilevel procedure which embeds the Recursive Multilevel Trust Region method [1] into an Augmented Lagrangian framework. Some results on both academic and industrial test cases are presented.**Source: **Congresso Biennale SIMAI MiniSimposio: MSP - Large-Scale Numerical Linear Algebra And Optimization, Torino, Italy, 25-28 June 2012

**See at: **
CNR ExploRA