Stress-constrained topology optimization of concrete structures:
A preliminary study for combining topology optimization and 3D printing

I. van de Werfhorst-Bouw, H. Hofmeyer, S. Boonstra, R.J.M. Wolfs

Eindhoven University of Technology, the Netherlands

Digital design tools for the 3D Concrete Printing (3DCP) industry could be enriched by topology optimization, among others to minimize the amount of concrete used. However, a prerequisite for applying such an algorithm to 3DCP is that concrete's asymmetric stress limits in tension and compression are correctly addressed. Therefore, here topology optimization is studied as the minimization of the structural volume, subject to local, asymmetric stress constraints, represented by the Drucker-Prager yield criterion. Three available methods have been selected for a comparison: Traditional Topology Optimization (TTO) in combination with the Method of Moving Asymptotes (MMA) by Svanberg (1987); Bi-directional Evolutionary Structural Optimization (BESO); and heuristic Proportional Topology Optimization (PTO). Numerical studies show that TTO provides more optimal results (i.e. a lower structural volume) than BESO and PTO. This is especially clearly shown by some typical benchmarks for which either pure tensile or pure compressive structures are generated. In these benchmarks, it is shown that BESO and PTO generally generate tension-only structures, whereas TTO generally provides more material-efficient compression-only structures. Moreover, TTO shows to be less sensitive to the presence and magnitude of peak stresses in the structure. As such, it is concluded that TTO is preferred over BESO and PTO. Consequently, TTO is applied in an illustrative case study of a two-dimensional facade structure, where a daylight score is presented as an objective or as an additional constraint, and a print path generation tool is applied to the topology optimization outcome. From this case study, although promising, it is concluded that more research is required to obtain a design-for-manufacturing tool that can be utilized in the 3DCP industry.

Key words: Topology optimization, 3D concrete printing (3DCP), BESO, PTO, traditional topology optimization, MMA, asymmetric stress constraints