On the Form Finding of Resilient and Sustainable Reinforced Concrete Structures
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The design of mechanically efficient structures significantly contributes to the sustainable transformation of the building sector. Numerical structural optimization provides powerful tools to support the achievement of this objective during early stages of the design process. Important criteria for the evaluation of mechanical performance are load transfer primarily by normal forces and material-appropriate layouts. This contribution presents the simultaneous optimization of structural geometry and local material properties in a SIMP-based topology optimization framework using the example of reinforced concrete structures. Concrete, the most common construction material, exhibits a pronounced tensile-compressive strength anisotropy with its compressive strength far exceeding its tensile capacity. The introduction of steel reinforcement to regions subjected to tensile loading mitigates this limitation. Contrasting to plain concrete, reinforced concrete displays anisotropic material behavior, as steel locally enhances material stiffness along its orientation, and thereby impacts the optimum structural geometry. To capture this behavior, local material properties are incorporated in the form finding by simultaneously optimizing the structural layout as well as the layout of the steel reinforcement. Reinforcement of tensile-loaded areas is achieved by the penalization of tensile strains within the optimization problem. Reinforced concrete is modelled using a smeared, macroscopic approach based on the theory of mixtures and the concept of volume fractions. The local material density, the steel reinforcement volume fraction, and its orientation serve as design variables within a FE discretized design domain. Numerical investigations reveal that the simultaneous optimization of structural geometry and material properties significantly impacts the resulting optimal layouts. The consideration of structural self-weight in the loading scenario strongly influences amount and distribution of steel reinforcement, underlining its importance for realistic and sustainable design. The method is applied to bridge design as a real-world example, demonstrating its potential for the conceptual design of resilient reinforced concrete structures.
