Abstract

This paper presents a family of finite elements for the nonlinear static and dynamic analysis of cables based on a mixed variational formulation in curvilinear coordinates and finite deformations. This formulation identifies stress measures, in the form of axial forces, and conjugate deformation measures for the nonlinear catenary problem. The continuity requirements lead to two distinct implementations: one with a continuous axial force distribution and one with a discontinuous. Two examples from the literature on nonlinear cable analysis are used to validate the proposed formulation for St Venant-Kirchhoff elastic materials. These studies show that displacements and axial forces are captured with high accuracy for both the static and the dynamic case.

Abstract

Recent seismic events occurred in areas rich of ancient remains and full of cultural and artistic heritage in terms of artworks. Earthquakes may damage buildings, but the vibrations may also induce the uplift and overturning of their content, implying irreparable loss of cultural values. The seismic assessment of objects is usually tackled modelling them as rigid blocks. This paper focuses on statues, which generally present a very complicated geometry, and proposes a general methodology involving different disciplines, for their experimental seismic assessment. The methodology is here applied to the masterpiece of “Paolo Orsi” museum in Syracuse (Italy), that is the “Venere Landolina”. Due to the complexity of statues, traditional techniques cannot be considered reliable for a proper geometry reconstruction; therefore, Terrestrial Laser Scanner (TLS) and Unmanned Aerial System (UAS) technologies are here employed to obtain a highly detailed and complete digital model. Aiming at providing a low-cost scaled physical model of the statue, a wooden specimen has been arranged employing a Computer Numerical Control (CNC) milling machine, cutting off disks from flat panels which are then superimposed and glued, progressively reconstructing the actual geometry of the statue. The specimen, able to approximately reproduce the scaled actual geometry, was then tested on a shaking table with ground motions compatible with those expected for the site where the statue is located. The obtained results are finally correlated with those expected for the real scale statue.

Abstract