Algebra, kinematics and compatibility of triangulated geometries | Funding Period 2
Innovative design strategies for material minimized carbon-reinforced concrete structures require the exploration of novel geometries. Project A04 is centered around the systematic generation of inspiring geometric structures accompanied by a rigorous mathematical analysis. The objective is to develop algebraic methods for deriving exact parametrizations of geometries, mathematical descriptions of designs for their assemblies, methods to analyze their dynamical properties, and methods to evaluate their suitability for applications.
A central theme is the investigation and generation of assemblies whose features typically depend on imposed constraints, e.g. contact between neighboring blocks of a structure. Symmetry principles are employed to construct regular assemblies from carefully designed blocks with a focus on the study of interlocking properties. These properties facilitate material minimized construction due to the self-supporting assembly of blocks. Another central theme are algebraic methods examining parameter-freeness and integrity properties of continuously parametrized building components.
Scientists
![[Translate to English:] Prof. Dr. Alice Niemeyer](/fileadmin/_processed_/e/e/csm_A_Niemeyer_Quadratisch_806ba9faca.jpg "Prof. Dr. Alice Niemeyer")
D-52062 Aachen (Germany)
52062 Aachen (Germany)
![[Translate to English:]](/fileadmin/_processed_/0/3/csm_A04_Stuettgen_quadratisch_Alvarez_0f3081c845.jpg "M.Sc. Sascha Stüttgen")
52062 Aachen
![[Translate to English:]](/fileadmin/_processed_/6/6/csm_A04_weiss_quadratisch_a26762cd9d.jpg "M.Sc. Meike Weiß")
D-52062 Aachen (Germany)
Cooperations
Ehemalige | Former involved
Tom Görtzen (research associate, RWTH Aachen, 07/2020 – 06/2024)
Construction and Stability of Piecewise Linear Structures with Free Boundary | Funding Period 1
In project A04, we inspire and provide suggestions to new constructions to other projects. The proposed constructions are calculated in an exact manner and can be modified in several ways. For instance, we can start with an arbitrary control triangle and use symmetries of a crystallographic group to create double periodic landscapes. Furthermore, we look at constructions bases on the idea of topological interlocking which describes interlocking 3D (convex) bodies without the use of any binder resulting in structures with high stability and resistance against vibrations and propagation of cracks. Concurrently, we look at theoretical problems linked with topological interlockings, suggesting an interdisciplinary approach. Among other things, we are planning to classify 3D interlockings. In particular, we strive to classify (a) simplicial surfaces with a given boundary and number of faces, and (b) 3D objects that allow a topological interlocking and can be embedded into a given simplicial surface.
3D model
This is the versatile block. Copies of this block can be assembled to generate complex assemblies which can lead to topological interlocking assemblies when putting additional constraints on some of the blocks.
Publikationen | Publications
Akpanya R.; Goertzen T.; Liu Y.; Stüttgen S.; Robertz D.; Xie Y. M.; Niemeyer A. C. (2024) Constructing Topological Interlocking Assemblies Based on an Aperiodic Monotile in: Proceedings of the Annual Symposium of the International Association for Shell and Spatial Structures (IASS)
Akpanya R.; Goertzen T.; Niemeyer A. C. (2024) From Tilings of Orientable Surfaces to Topological Interlocking Assemblies in: Applied Sciences – DOI: 10.3390/app14167276
Akpanya, R.; Goertzen, T.; Wiesenhuetter, S.; Niemeyer, A. C.; Noennig, J. (2023) Topological Interlocking, Truchet Tiles and Self-Assemblies: A Construction-Kit for Civil Engineering Design in: Holdener, J.; Torrence, E.; Fong, C.; Seaton, K. [eds.] Proceedings of Bridges 2023: Mathematics, Art, Music, Architecture, Culture, 27.–31.07.2023 in Halifax (Nova Scotia, Canada), Phoenix: Tessellations Publ., p. 61–68.
Akpanya R.; Goertzen T.; Niemeyer A. C. (2023) A Group-Theoretic Approach for Constructing Spherical-Interlocking Assemblies in: Proceedings of the Annual Symposium of the International Association for Shell and Spatial Structures (IASS)
Chudoba, R.; Niemeyer, A. C.; Spartali, H.; Robertz, D.; Plesken, W. (2021) Description of the origami waterbomb cell kinematics as a basis for the design of thin-walled oricrete shells in: Behnejad, A.; Parke, G.; Samavati, O. [eds.] Inspiring the Next Generation – Proceedings of IASS 2020/21, 23.–27.08.2021 in Guildford (UK), p. 2681–2689 – DOI: 10.5281/zenodo.6759486
Curosu V.; Kikis G.; Krüger C.; Liebold F.; Macek D.; Mester L.; Platen J.; Ritzert S.; Stüttgen S.; Kaliske M.; Klinkel S.; Loehnert S.; Maas H.-G.; Stefanie Reese; Daniel Robertz (2023) Ansätze für numerische Methoden zur Inspiration, Analyse und Bewertung neuartiger Carbonbetonstrukturen in: Bauingenieur 98, issue 11, p. 368–377 – DOI: 10.37544/0005-6650-2023-11-56
Goertzen T.; Macek D.; Schnelle L.; Weiß M.; Reese S.; Holthusen H.; Niemeyer A. C. (2025) Influence of block arrangement on mechanical performance in topological interlocking assemblies: A study of the versatile block in: International Journal of Solids and Structures 306 (2025) – DOI: https://doi.org/10.1016/j.ijsolstr.2024.113102
Goertzen, T.; Niemeyer, A. C.; Plesken, W. (2022) Topological Interlocking via Symmetry in: Stokkeland, S.; Braarud, H. C. [eds.] Concrete Innovation for Sustainability – Proc. for the 6th fib International Congress 2022, 12.–16.06.2022 in Oslo (Norway), Oslo: Novus Press, p. 1235–1244.
Neef T.; Goertzen T.; Niemeyer A. C.; Mechtcherine V. (2024) Materialsparende Betondecke aus 3D-gedruckten Verriegelungsblöcken in: Beton- und Stahlbetonbau, p. 882–893 – DOI: https://doi.org/10.1002/best.202400061
Robertz, D.; Spartali, H.; Chudoba, R.; Plesken, W.; Niemeyer, A. C. (2022) Semi-symmetric origami waterbomb cell kinematics and tessellation for the design of thin-walled folded shells in: Su-duo Xue, S.-d.; Wu, J.-z.; Sun, G.-j. [eds.] Innovation, Sustainability and Legacy – Proceedings of IASS/APCS 2022, 19.–22.09.2022 in Beijing (China), p. 2314–2324.
Stüttgen, S.; Akpanya, R.; Beckmann, B.; Chudoba, R.; Robertz, D.; Niemeyer, A. C. (2023)Modular Construction of Topological Interlocking Blocks—An Algebraic Approach for Resource-Efficient Carbon-Reinforced Concrete Structures in Buildings 13, issue 10, 2565 – DOI: https://doi.org/10.3390/buildings13102565
Vakaliuk, I.; Goertzen, T.; Scheerer, S.; Niemeyer, A. C.; Curbach, M. (2022) Initial numerical development of design procedures for TRC bioinspired shells in: Su-duo Xue, S.-d.; Wu, J.-z.; Sun, G.-j. [eds.] Innovation, Sustainability and Legacy – Proceedings of IASS/APCS 2022, 19.–22.09.2022 in Beijing (China), p. 2597–2608.
Wiesenhuetter, S.; Goertzen, T.; Vakaliuk, I.; Curbach, M.; Scheerer, S.; Niemeyer, A. C.; Noennig, J. R. (2023) Triply Periodic Minimal Surfaces – A Novel Design Approach for Lightweight CRC Structures in: Ilki, A.; Çavunt, D.; Çavunt, Y. S. [eds.] Building for the Future: Durable, Sustainable, Resilient – Proc. of fib Symposium 2023, 05.–07.06.2023 in Istanbul (Turkey), publ. in: Lecture Notes in Civil Engineering, Vol 350, Cham: Springer, p. 1449–1458 – DOI: 10.1007/978-3-031-32511-3_148