Grammar-based Generation of Highly Constrained Trusses
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In the design of in-plane loaded reinforced concrete structures, a truss analogy based on the lower bound theorem of the theory of plasticity, known as strut-and-tie models, is often used, particularly in the case of complex geometries. Suitable truss models must satisfy the equilibrium and static boundary conditions and should further take into account practical considerations such as constructability, e.g. the preference towards orthogonal reinforcement. As a result, deriving suitable truss models becomes a highly constrained problem, whereby manual generation requires considerable experience and time. Previous attempts at automation are based on either discrete layout or continuous topology optimisation, with the former struggling to account for user adaptations as well as varying initial ground structures, and the latter for constructability concerns. In this work, we propose a grammar-based framework that imposes strict and constraining rules to reduce the design space and integrate engineering expertise with the goal of facilitating the generation of a variety of suitable, near-optimal trusses. Similar to a graph grammar, the graph representing the truss undergoes production rules at each iteration, allowing for human-computer interaction. This framework is illustrated with a case study of a reinforced concrete wall with an opening and a concentrated load, where two trusses are generated with different objectives in terms of material usage and constructability. We demonstrate that these trusses can be decomposed into a sequence of rules, effectively simulating the engineer's design process. This contribution paves the way for future research into AI-assisted inference of strut-and-tie models for complex reinforced concrete structures, as well as generative modelling of truss geometries at large.