Optimized strut-and-tie design for double-sided corbels using multi-material topology optimization under multiple load cases

Designing structures often relies on the experience of engineers, involving an iterative process to achieve a balance between cost-effectiveness, durability, reliability, and to fulfill the required specifications. In this context, this paper introduces a novel multi-material topology optimization approach for reinforced concrete structures with D regions, considering multiple load cases during the optimization process. The methodology adopts a two-loop approach. The first loop minimizes the structure's compliance to reduce weight within a given material volume constraint. The second loop iteratively replaces concrete exceeding the Ottosen four-parameter failure surface by steel, ensuring a safe stress level under a stress constraint. The required steel area is determined based on the equivalent principal forces in finite elements classified as steel in the resulting topology from the multiple load cases. Finally, a nonlinear comparative analysis considering both material and geometric nonlinearity of the optimized and reference structures is performed using Simulia Abaqus. This analysis evaluates the crack pattern, stress distribution, and the yielding of the reinforcement up to the ultimate load of the structure. The outcomes demonstrate lightweight designs meeting the required structural performance standards.