Robust design optimization of three-dimensional concrete building components.

In engineering practice, structures are typically designed to have a minimal weight or cost, while satisfying all safety and serviceability constraints. These constraints can for example be the load-bearing capacity or deflection of a structure, or limiting the amount of damage or stress in the structure.

In general, the design of structures follows either a performance-based or a code-based approach. With performance-based design, the mechanical behavior of a structure is modeled, using for example nonlinear material models. The load-bearing capacity of a structure can for example be assessed by simulating the evolution of cracks or damage when a load is applied. Code-based design is a more generalized and conservative design approach, which relies on a set of rules instead of elaborate nonlinear material models. Complex processes such as cracking are simplified into generally applicable design rules, based on a statistical analysis of elaborate simulations and experimental results. Examples of such building codes are the European `Eurocodes' or the American Standards for Civil Engineering (ASCE).

For this study, we consider the numerical optimization of structures, following both a performance-based and a code-based approach. This work focuses primarily on the optimization of ribbed floors, but other structures are also considered.

The first part of this study focuses on the performance-based structural optimization of ribbed floors and simpler two-dimensional structures. The topology, size, and shape of a structure is optimized to have a minimal weight while guaranteeing a predefined load-bearing capacity, considering the softening behavior of quasi-brittle materials. For the ribbed floors, the rib pattern is optimized with topology optimization to obtain free-form geometries. We also use a feature mapping approach to control the complexity of the optimized designs, which allows to investigate the influence of the design freedom or complexity on the material efficiency of the optimized design.

The second part of this study focuses on code-based structural optimization, by optimizing the size and shape of one-way and two-way reinforced concrete ribbed floor slabs according to the Eurocodes. The optimization algorithm searches for the design with the lowest possible material cost, while satisfying all relevant constraints from the Eurocodes. The optimization of the one-way ribbed floor slab considers two scenarios: shape optimization of a free-form rib geometry and size optimization of simple prismatic ribs. For the two-way ribbed floors, also called waffle slabs, 9 scenarios with increasing complexity are considered, by combining shape and/or size optimization of the ribs with size optimization of the steel reinforcement.

Results show that the methodologies for performance-based and code-based design lead to feasible designs. In the code-based optimization, it is shown that using a finite difference sensitivity analysis can be a pragmatic solution for realistic Eurocode-based optimization problems, with acceptable computation time. When optimizing waffle slabs with different scenarios of increasing design freedom, it is shown that optimized designs with total design freedom are often only marginally better than designs with more limited design freedom and complexity. Since a simpler design is typically easier and cheaper to manufacture, it is up to the designer to consider factors such as manufacturability and choose an appropriate optimized design accordingly.

A full-scale prototype of an optimized waffle slab is manufactured to demonstrate the practical feasibility and manufacturability of the design. The prototype has been subjected to a proof loading to compare the theoretically expected load-bearing capacity with the experimental results.