Keywords: masonry-like materials, nonlinear dynamics, numerical methods.

Numerical tools for modelling masonry buildings subjected to time-dependent loads have a proven, important role in assessing the seismic vulnerability of historical constructions. The two main aspects that need to be addressed in studying the dynamic behaviour of masonry structures 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 constitutive equation for masonry materials models masonry as a nonlinear elastic material with zero tensile strength and infinite compressive strength. This constitutive equation, which is known as the masonry-like (or no-tension) model, has been generalized in order to take into account the bounded compressive strength of masonry materials [1]. The equation has subsequently been implemented in the finite element code NOSA [1], developed at ISTI-CNR and successfully applied to the static analysis of several historical masonry buildings, and more recently to the dynamic analysis of masonry beams and towers.

Recent efforts have been directed at developing simplified constitutive models for masonry structures by representing them through one-dimensional elements. Such efforts have given rise to a nonlinear constitutive equation for beams, in which the generalized stress (normal force and bending moment) is a function of the generalized strain (extensional strain and curvature change of the beam's longitudinal axis) [2]. This constitutive model is based on the assumption that the material does not withstand tensile stresses in the longitudinal direction. Variants of the model take into account cases of unbounded as well as bounded compressive strength. The model has been extended to deal with both solid and hollow rectangular cross-sections in order to study masonry arches and freestanding towers [3]. The resulting constitutive equation has been implemented in the numerical code MADY, developed at the Department for Construction and Restoration of the University of Florence to perform nonlinear dynamic analyses of slender masonry structures.

This paper is devoted to comparing the models implemented in the two finite element codes NOSA and MADY, which are applied to the dynamic problem of a masonry tower with hollow rectangular cross-section subjected to its own weight and an accelerogram recorded during the Nocera Umbra earthquake. The solutions obtained using the two different models are compared in order to highlight the similarities and differences between the numerical procedures proposed.

1

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

2

N. Zani, "A constitutive equation and a closed-form solution for no-tension beams with limited compressive strength", Eur. J. Mech. A/Solids, 23/3, 467-484, 2004. doi:10.1016/j.euromechsol.2004.01.008

3

M. Lucchesi, B. Pintucchi, "A numerical model for non-linear dynamic analysis of slender masonry structures", European Journal of Mechanics A/Solids, 26, 88-105, 2007. doi:10.1016/j.euromechsol.2006.02.005

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