The NOSA finite element code allows for: 1) Static and dynamic analysis of masonry structures using various material models like elasticity, composite, elasto-plasticity, and masonry-like materials. 2) Modeling of different structural elements like beams, shells, and plates with various interpolation functions. 3) Assessment of strengthening interventions on historic masonry buildings before implementation to determine effectiveness. 4) Application to analysis of several historic Italian buildings to evaluate safety, crack patterns, and effects of differential settlement.

1. Istituto di Scienza e Tecnologie
dell’Informazione “A. Faedo”
THE FINITE ELEMENT CODE NOSA
FOR NONLINEAR STRUCTURAL ANALYSIS
Material models
ELASTICITY: static and dynamic analysis
COMPOSITE: shell and beam elements have layers with different
mechanical and thermal properties
ELASTO-PLASTICITY: static and dynamic analysis
MASONRY-LIKE: static and dynamic analysis
HEAT TRANSFER

2. Element library of the NOSA code
Structural type Element Interpolating Remarks
identifier functions
number
3D element 1 quadratic 20 nodes
isoparametric
element
Plane stress 2 quadratic 8 nodes
element isoparametric
element
Plane strain 3 quadratic 8 nodes
element isoparametric
element
Axisymmetric 4 quadratic 8 nodes
element isoparametric
element
Thin shell 5 Linear for 8 nodes
element displacements, isoparametric
quadratic for element
rotations

3. Structural type Element Interpolating Remarks
identifier functions
number
Plane strain 6 linear 4 nodes
element isoparametric
element
Axisymmetric 7 linear 4 nodes
element isoparametric
element
3D element 8 linear 8 nodes
isoparametric
element
Straight beam 9 linear 2 nodes
element isoparametric
element
Thick shell 10 Linear for 4 nodes
element displacements isoparametric
and rotations element

4. Structural type Element Interpolating Remarks
identifier functions
number
Plane heat 11 quadratic 8 nodes
transfer isoparametric
element element
Plane heat 12 linear 4 nodes
transfer isoparametric
element element
Axisymmetric 13 quadratic 8 nodes
heat transfer isoparametric
element element
Axisymmetric 14 linear 4 nodes
heat transfer isoparametric
element element
3D heat 15 linear 8 nodes
transfer isoparametric
element element

5. Flow-chart for NOSA (nonlinear static analysis)

6. THE FINITE ELEMENT CODE NOSA FOR THE STRUCTURAL
ANALYSIS OF HISTORIC MASONRY CONSTRUCTIONS
Static and dynamic analysis
Limit analysis
Thermo-mechanical analysis of masonry structures subjected to thermal variations
Modelling of strengthening
operations (fitting of metallic
Beams and rings, retaining structures, etc.)

7. NOSA has been successfully applied to the analysis of some
buildings of historical and architectural interest:
The baptistery of the Volterra cathedral (1995)
The stress field in the dome has been
calculated with the aim of assessing the
effectiveness of the existing metallic rings.
The finite element mesh

8. The Medici Arsenal, Pisa (1996)
The study is aimed at determining the static
behaviour of the structure dating back to the
XIII century and constituted by twelve series of
arches. In particular, some strengthening
interventions have been modelled and compared
in order to assess their effects on the static
safety and seismic resistence of the
construction.
The arches of the Arsenal

9. The Goldoni theatre, Livorno (1998)
The static behaviour of
the scenic arch has
been assessed.

10. The S. Nicolò cathedral, Noto (1998)
The static behaviour of the right
longitudinal wall of the nave has been
analysed with the aim of determining the
effects of differential settling of the
pillars.
The longitudinal wall

11. The Buti bell tower (2004)
A static analysis of the bell tower subjected to its
own weight and a horizontal load simulating a
seismic action has been conducted with the aim
of determining the origins of the cracks.
Crack distribution in the tower

12. The church of San Pietro in Vinculisa, Pisa (2003)
The right longitudinal
wall of the wall has
been analysied with
the aim of assessing
the effect of
differential settlings
of the pillar on the
stress field and crack
distribution .
Crack distribution in a longitudinal wall

13. The church of Santa Maria Maddalena, Morano Calabro (2004-2005)
A static analysis of the dome and the drum has
been conducted with the aim of assessing the
effects of both differential settlings of the drum
and a horizontal load on the stress field and
crack distribution in the dome.
Crack distribution in the dome

14. The church of San Ponziano, Lucca (2005, 2007)
Static and dynamic
analyses of the cross
vault overlooking the
altar have been
conducted by taking
the presence of the
metallic tie-rods into
account.
Finite element discretization of the vault

15. The church of Santa Maria della Roccella, Roccelletta Borgia (2009)
The study aims at analyse the
sesimic vulnerability of the
structure and take into account the
regulations provided by the
Ministry of Cultural Heritage in
2007 concerning the assessment
and reduction of the seismic risk of
the historical buildings.
Dynamic analysis of the church

16. The Rognosa tower, San Gimignano (2008-2011)
The study concerns the static behaviour and the
seismic vulnerability of the Rognosa tower, added to
the Unesco World Heritage List in 1990. The
behaviour of the tower subjected to its own weight
and an accelerogram recorded during a real
earthquake, is investigated.

17. The tower of the Hours, Lucca (2010)
The analysis aims at assessing
the dynamic beaviour of the
tower in the presence of time-
dependent loads modelling
seismic actions.
Finite element discretization of the tower

18. - The finite element code NOSA allows:
- to determine the static and dynamic behaviour of masonry buildings
- to model strengthening interventions and assess their effectiveness
before implementation
Therefore, NOSA can be used in the field of maintenance
and safeguarding of the national architectural heritage to
assess the safety of artistically important masonry
buildings and to optimise potential maintenance and
strengthening operations in terms of architectural impact
and static effectiveness.
COMES-NOSA is a freeware version of NOSA for the nonlinear static
analysis of masonry buildings
http://www.isti.cnr.it/research/unit.php?unit=MMS&section=software