MS1.9 - Advances in Computational Structural Dynamics

Permanent residual drift is the structural response parameter most easily collected during post-earthquake assessments. Its importance has been proven by many past earthquakes where it has been used to determine the demolition of a number of structures after their residual drifts had exceeded certain limit values, even if they did not show evident signs of severe damage. However, general studies on seismic residual drift demands are far less common than, the more popular, transient maximum drift demand. One of the reasons for this rarity is the more demanding computational times required for the residual drift assessment. To this end, we offer a hybrid data-driven predictive model for the residual drift demand purposed for performance assessment of Steel Moment Resisting Frames (SMRF). The hybrid model presented here is chosen to strike a good balance between a mechanics-based model, whose accuracy is low, and the data-driven model, whose interpretation is difficult. This proposed model is based on a database generated by nonlinear response history analyses (NRHA) of 24 deteriorating SMRFs under 596 ground-motion records, covering two different sites, resulting in more than 14,000 structural responses database. The behaviour of the residual drift demand is also studied from the results of NRHA. The development of the model is preceded by an extensive feature selection process employing several Machine Learning (ML) algorithms, considering structural and seismic parameters as well as key static response features. More importantly, it is found that the available seismic codes and past studies regarding residual drift demand to date overlooked the issue of hazard consistency, which enables the connection between seismic hazard level and the corresponding ground motion suite used to have a meaningful structural performance assessment. Therefore, we use the Conditional Scenario Spectra method, which generates a set of realistic earthquake spectra with a corresponding assigned rate of occurrences based on their spectral shape and intensity, hence, preserving the critical relationship of hazard consistency.

Homogenization of periodic media, which are characterized by a modular repetition along one direction of a unitary cell, can be conveniently used to model beam-like structures as equivalent continua. This is the case of lattice structures, as well as multi-story tower-buildings. As regards the latter, in several recent papers, buildings and towers with a uniform geometry along the height were macroscopically modelled as shear-shear-torsional beams. Especially, in a literature paper of Luongo and Zulli (Meccanica, 55(4), 907-925), a homogeneous shear beam model was proposed to address the free and forced dynamic behaviour of a multi-story building. The equations of motion for a damped system were derived, where only the special case of proportional damping was considered, according to the Rayleigh model. First, the free dynamics was investigated, highlighting the interesting organization of the natural frequencies and modes in triplets, as functions of the wave-number. Then, on the base of the latter, a solution strategy was proposed in the framework of the perturbation theory. Here, the case of a multi-story building is analysed, where visco-elastic devices are added to passively control its response. To this aim, the equations of motion of the shear-shear-torsional beam model (described in the paper of Luongo and Zulli) are consistently modified, involving a non-proportional damping model. It derives by the addition of spring-dashpot systems placed in-parallel to the columns; it is found that, although dashpots lead to a proportional damping matrix, the resultant damping is of non-proportional type, as they are added to a building. As a consequence, the equations of motion result in coupled partial differential equations. The solution is assumed as trial series in the normal coordinates, from which a set of infinite triplets of ordinary differential equations is derived. Each triplet is formed by coupled scalar equations and governs the evolution of the three cross-section modes associated to the same wave-number; however, triplets are uncoupled among them. It is observed that damping couples the cross-section dependence of modes, i.e. inside the single triplet, differently than what happens in the proportional damping case. A numerical example on a case study is proposed, where the analytical results of the homogeneous model are compared with those of a refined model implemented in a commercial F.E.M. software.

Buildings subject to natural hazards should be considered as a system composed of structural elements and non-structural components. This is crucial for resilience assessments where the damage of both structural and nonstructural components can lead to loss of functionality and affect robustness. Most traditional modeling frameworks only account for the behavior of structural systems or use cascaded methods to study the behavior of nonstructural elements [1]. Here we discuss the simulation framework we are developing to simulate the entire building comprising both structural and nonstructural components. The framework is based on the potential of mean force approach to Lattice Element Method (LEM), used for modeling fracture in heterogeneous materials [2]. The discrete nature of LEM is particularly advantageous for damage and failure assessment as it does not suffer from the limitations of the classical continuum approaches in modeling discontinuity. We calibrate the parameters of interaction potential for one- and two-dimensional members. The computational tool is shown to be accurate and efficient for quasi static simulations. This is essential to make the simulation tool amenable to resilience assessments under natural hazards with dynamic nature such as earthquakes and hurricanes. To evaluate versatility of the proposed approach in simulating the dynamic response of the buildings, we leverage the fundamental of molecular dynamics within the PMF-based LEM framework. Analogous to static condensation in continuum mechanics, here, at every single time step, the mass-included degrees of freedom are updated and obtained through MD algorithm while the LEM formulation obtain the remaining degrees of freedom evoking theorem of minimum potential energy. In this presentation, we discuss the adaptation of MD to LEM formulation to account for dynamic effects. The promise of the dynamic extension of the PMF-based LEM is then evaluated through its application to free vibration analysis of the large-scale buildings. This is essential to make the simulation tool amenable to resilience assessments under natural hazards with dynamic nature such as earthquakes and hurricanes.