TOWARDS THE OPTIMIZATION OF REINFORCED CONCRETE SLAB TOPOLOGY

The paper addresses the problem of optimizing the thickness distribution of reinforced concrete floor slabs through an iterative numerical approach based on the finite element method (FEM). Structural optimization is a long-standing research domain, beginning with classical formulations such as Michell’s fully stressed truss layouts and Rozvany’s theory of optimal layout, and further developed into modern topology optimization methods. The study provides a review of the theoretical background of structural optimization, with particular emphasis on the SIMP (Solid Isotropic Material with Penalization) and ESO (Evolutionary Structural Optimization) approaches, which represent the state-of-the-art techniques for material distribution problems. Within this framework, the authors propose and implement an iterative algorithm that modifies the slab thickness at each step depending on the stress state of the finite elements. The algorithm was developed and executed in the RFEM 6 environment using the RF-COM/WEB Services API and Python scripting, which allows automated recalculation and modification of both geometric and mechanical properties. The case study focuses on a square reinforced concrete slab measuring 3×3 m, discretized into 900 finite elements and supported along the contour by hinges. For simplicity, the material is initially modeled as isotropic with an elastic modulus of 20 GPa and an ultimate strength of 15 MPa. The von Mises stress criterion is employed to assess element performance relative to the strength limit. The optimization procedure begins with a uniform initial thickness of 200 mm across the slab. During each iteration, FEM analysis determines the stress distribution, after which the thickness of elements is updated: increased where stresses approach or exceed the allowable value and decreased where large strength reserves remain. A fixed step of 20 mm was applied for thickness adjustments, and convergence was achieved after 10 iterations. The final design demonstrates a rational redistribution of material—thickness is concentrated in highly stressed regions while low-stress areas are thinned—leading to a more material-efficient slab design. The developed method can be viewed as a free-size optimization procedure, closely related to the ESO/BESO concept, but formulated in terms of element thickness rather than material removal or addition. The study highlights potential improvements to the algorithm, such as gradient-based optimization, adaptive step sizes, and smoothing techniques to ensure stable convergence. Furthermore, the research outlines prospects for extending the method to anisotropic and heterogeneous materials such as reinforced concrete, where both concrete and reinforcement contribute to the structural response. The results demonstrate the practical feasibility of iterative thickness optimization for slabs and underline the potential for integrating such algorithms into automated design workflows. The approach provides a pathway toward lighter, more economical reinforced concrete slabs that meet strength requirements while reducing material consumption, which is essential in the context of sustainable construction practices.