Computational Limit Analysis algorithms for large-scale truss-frame structures with interaction domain

The contribution revisits two recently developed computational algorithms for Limit Analysis (LA) aimed at predicting the elastoplastic response of large-scale 3D truss-frame structures [1]. The first LA algorithm accurately traces the piece-wise linear elastoplastic evolutive response of a structure up to plastic collapse [2], while the second deploys an iterative kinematic approach to directly determine the collapse characteristics based on the upper-bound theorem of LA [3], both being based on a boxed-form Rankine-type interaction domain, in the space of internal variables. Herein, the kinematic algorithm is presented in an enhanced version, capable of handling an ellipsoidal yield domain, specifically with axial force and bending moments interaction, and potentially coupling other static internal actions. The potentiality of such improvements also relies on the possibility to offer comparative insights related to structural LA, particularly with respect to results for uncoupled Rankine-type yield domains inscribed within or circumscribed around an ellipsoidal interaction domain. The manuscript first evaluates the load-bearing capacities of a large-scale structure with over 4000 degrees of freedom, using the enhanced versions of the LA algorithms to model the remarkable arch of historical San Michele Bridge (Italy, 1889). A particular focus is then placed on demonstrating the advantages of considering both coupled (hyper-ellipsoidal) and uncoupled (Rankine-type) yield domains represented in the space of static variables governing the problem. To this end, a simplified space truss-frame cantilever beam is further analyzed, under varying loading conditions leading to bending and torsion, and allowing also for analytical treatment. Insights gained from this simplified case study are subsequently applied to refine and deepen the interpretation of the bridge arch analysis results. The inherent peculiarities herein highlighted in relation to the devised computational LA algorithms shall significantly expand their applicability, making them highly effective for practical truss-frame analysis and realworld professional applications, truly accounting for structural bearing capacity, toward complying with current demands for resilience-focused design and assessment, in different structural contexts.