Keywords: masonry arches, nonlinear elasticity, dynamic analysis, finite-element method.

The modelling of masonry structures subjected to time-dependent loads is crucial in assessing their mechanical behaviour in the presence of earthquakes, as well as in planning suitable strengthening and restoration operations. The main aspects of the modelling are the choice of the constitutive equation for masonry materials, whose mechanical properties depend heavily on its constituent elements and the building techniques used, and the formulation of suitable numerical techniques for integrating the equations of the motion. The finite-element method is widely employed for numerical solution of the dynamic problem of large, complex masonry structures, though the debate on the choice of constitutive equations able to realistically model the behaviour of masonry materials is still open.

A constitutive equation for masonry materials is proposed in [1,2,3], where the masonry is modelled as a nonlinear elastic material with zero tensile strength and infinite compressive strength. This constitutive equation, which is known as the masonry-like model, has been implemented in the finite element code NOSA, successfully applied to the static analysis of several historic masonry building [3] and to the dynamic analysis of masonry pillars [4], beams [5] and domes [6].

In the present paper we recall the constitutive equation of masonry-like materials with bounded compressive strength introduced in [3] and present the results of the dynamic analysis of a circular masonry arch subjected to its own weight and sinusoidal accelerations of variable frequency, conducted with the code NOSA [3]. The differences between the linear and nonlinear behaviours are highlighted and the dependence of the solution on some parameters, such as excitation frequency and compressive strength, is analysed.

1

G. Del Piero, "Constitutive equation and compatibility of the external loads for linear elastic masonry-like materials", Meccanica, 24, 150-162, 1989. doi:10.1007/BF01559418

2

S. Di Pasquale, "New trends in the analysis of masonry structures", Meccanica, 27, 173-184, 1992. doi:10.1007/BF00430043

3

M. Lucchesi, C. Padovani, G. Pasquinelli, N. Zani, "Masonry constructions: mechanical models and numerical applications", Lecture Notes in Applied and Computational Mechanics, Vol. 39, Springer-Verlag, Berlin Heidelberg, 2008.

4

S. Degl'Innocenti, M. Lucchesi, C. Padovani, A. Pagni, G. Pasquinelli, N. Zani, "Dynamical analysis of masonry pillars", Third International Congress on "Science and Technology for the Safeguard of Cultural Heritage in the Mediterranean Basin", Alcalá de Henares, Spain, 9-14 July 2001.

5

S. Degl'Innocenti, C. Padovani, G. Pasquinelli, "Numerical methods for the dynamic analysis of masonry structures", Structural Engineering and Mechanics, 22(1), 107-130, 2006.

6

S. Degl'Innocenti, C. Padovani, A. Pagni, G. Pasquinelli, "Dynamic Analysis of Age-Old Masonry Constructions", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 79, 2006. doi:10.4203/ccp.83.79

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