3D Truss-Continuum Topology Optimization with Demolding Constraint of Prestressed Concrete Floors
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As the most manufactured material in the modern history, concrete remains widely used the construction industry \cite{elhacham_global_2020}. Within this field, Prestressed concrete (PC) is increasingly favored over reinforced concrete (RC) due to its efficient uses in concrete's compressive strength and reductions in members' depths while maintaining their structural performances \cite{edward_g_navy_prestressed_2009}. Even though the benefits are substantial, the fact that cement, the main component in concrete structures, contributes to 5\% of global man-made CO2 emission \cite{iea_cement_2009} still lingers and the reduction of concrete consumption is recommended \cite{globalABC_global_2020}. This work presents an algorithm to optimize PC floors using topology optimization (TO). TO algorithm has been shown to be able to optimize RC structures for maximum structural stiffness under a volumetric constraint \cite{jewett_comparing_2024}. However, the state of the art of TO of PC elements focuses on 2D elements which limited the application to beams and 2D-like structures \cite{amir_simultaneous_2018, shobeiri_topology_nodate}. This leaves out other carbon intensive elements such as two-way floors \cite{huberman_optimizing_2015}. Moreover, while TO with the demolding constraint have shown to improve the manufacturability of the designs, it has not been applied to the context of PC floor design \cite{vatanabe_topology_2016}. Therefore, we seek to answer the question on how we can use TO to maximize structural stiffness of PC floors with demolding constraint. To answer the question, this work consists of (i) a 3D domain of truss-continuum elements which directly represent the PC floor, (ii) an asymmetric material model to accurately represent concrete and reinforcement material behavior, and (iii) a demolding constraints on the structures, making it possible to manufacture the optimized structures using the traditional casting-demolding method. The numerical results will demonstrate the effect of prestressing tendons on the floor designs and explore prestressed tendon layout and trade-off between fabrication complexity and structural performance.
