Speaker
Description
Non-Smooth Contact Dynamics (NSCD) is a well-established method for the dynamic analysis of rigid bodies and has recently been extended to historical masonry structures, where the arrangement of units has a strong influence on the global response. While most of the existing formulations assume prismatic block geometries, several historical structures are composed of elements with curved shapes (for instance, arches and vaults), for which the accurate representation of geometry is fundamental.
In this contribution, a NSCD-based computational strategy is proposed in which curved rigid blocks are described using a NURBS-based geometric formulation (where NURBS denotes Non-Uniform Rational B-Spline). Each block is modelled as a closed solid defined by NURBS boundary surfaces, providing the exact representation of geometry and accurate determination of inertial properties via surface integration. The dynamic response of the system is governed by the impulse–momentum balance at the block level, where external actions and contact interactions induce variations in the velocity field over the discrete time steps. Normal and tangential contact impulses are introduced at block interfaces and governed by a frictional contact law. The contact detection between curved bodies is carried out by combining the Gilbert-Johnson-Keerthi (GJK) distance algorithm with a point-inversion procedure conceived for NURBS surfaces. At each time increment, the resulting non-smooth dynamic problem is written as a second-order conic programming (SOCP) problem, whose solution provides the admissible block velocities with respect to contact and frictional constraints.
The proposed formulations highlight the link between structural dynamics, convex optimization, and geometry. This approach seems particularly suited for analysis of the responses of historical masonry structures to dynamic actions.