Simultaneous shape and topology optimization of prestressed concrete beams

This paper presents a new optimization approach for the design of prestressed concrete beams. The prestressing tendon is modeled as a chain of linear segments that transfer point forces to the concrete domain according to the tendon’s angles. The concrete beam is modeled as a discretized continuum following density-based approaches to topology optimization. The shape of the tendon and the topology of the surrounding concrete are optimized simultaneously within a single problem formulation. A special filtering technique is developed in order to ensure that the tendon is covered by concrete, thus shape and topological variables are tightly coupled. Several test cases demonstrate the applicability of the proposed optimization procedure. The deformation of the optimized designs due to external loads is counteracted by the deformation due to prestressing, hence by tuning the force in the tendon the total deformation can approach zero. Consequently, the beams exhibit a compression-only response meaning that the common goal of prestressed concrete design is achieved.