Topology and shape optimization of 3D prestressed concrete structures

In this paper, we introduce a computational framework for optimizing 3D prestressed concrete structures. The procedure combines shape optimization of post-tensioning cables with topology optimization of concrete, enabling novel design configurations of 3D beams and plates. Prestressing cables are modeled as B-spline curves that are embedded within a concrete continuum and whose control points serve as design variables. Concurrently, the distribution of concrete is determined by density-based topology optimization. A special filter enforces concrete cover around the cables, creating a coupling between the two sets of design variables. The optimization problem formulation mimics the design intent of prestressed concrete structures, separating the load-balancing part with respect to permanent loads from stiffness maximization with respect to live loads. Results show that material savings exceeding 30% can be achieved compared to solid prestressed members, strengthening the argument in favor of using prestressed concrete for reducing embodied CO2. The complete implementation in MATLAB is provided as supplementary material.