Distributed redundancy in structural systems

Image: Dr.-Ing. Jan Gade
Representation of the redundancy density of the Carola Bridge in Dresden based on the distributed redundancy analysis

Based on analogy considerations between minimum principles in geodesy and statics [1], the so-called redundancy factors for trusses and frame structures were first described in the 1990s [2, 3]. A redundancy fraction quantifies the contribution of the associated structural element or load transfer mode to the degree of static indeterminacy of the system, so that this system variable can be specified as a spatial distribution in the structure [2-7]. Knowledge of this spatial distribution provides valuable insights into the load-bearing behavior of a system and can be used, among other things, to assess failure safety.

There are a number of works that address the utilization of redundancy distribution for structural assessment and design. These include the design of adaptive structures [8] as well as the assessment of robustness and the consideration of the assembly capability of a structure [9].

The concept of distributed redundancy and essential properties of the descriptive variables are being further researched at the department.

 

References:

[1] Klaus Linkwitz. "Fehlertheorie und Ausgleichung von Streckennetzen nach der Theorie elastischer Systeme". Deutsche Geodatische Kommission bei der Bayerischen Akademie der Wissenschaften, Reihe C: Dissertationen No. C 46. Beck. 1961.

[2] Joachim Bahndorf. "Zur Systematisierung der Seilnetzberechnung und zur Optimierung von Seilnetzen". Dissertation, Universität Stuttgart, Beck Verlag, 1991.

[3] Dieter Ströbel. "Die Anwendung der Ausgleichungsrechnung auf elastomechanische Systeme". Dissertation, Universität Stuttgart, Beck Verlag, 1997.

[4] Malte von Scheven, Ekkehard Ramm und Manfred Bischoff. "Quantification of the redundancy distribution in truss and beam structures". In: International Journal of Solids and Structures 213, pp. 41–49. 2021. doi: 10.1016/j.ijsolstr.2020.11.002

[5] Jan Gade, Anton Tkachuk, Malte von Scheven und Manfred Bischoff. ”A continuum-mechanical theory of redundancy in elastostatic structures“. In: International Journal of Solids and Structures 226-227, 110977, S. 1–16. 2021. doi: 10.1016/j.ijsolstr.2021.01.022.

[6] Florian Geiger. "Strukturmechanische Charakterisierung von Stabtragwerken für den Entwurf adaptiver Tragwerke". Doktorarbeit, Nr. 74, Universität Stuttgart. 2022. doi: 10.18419/opus-12299

[7] Jan Gade. "Distributed Redundancy in Elastostatics for the Design of Adaptive Structures". Doktorarbeit, Nr. 78, Universität Stuttgart. 2024. doi: 10.18419/opus-15141

[8] Julia Laura Wagner, Jan Gade, Michael Heidingsfeld, Florian Geiger, Malte von Scheven, Michael Böhm, Manfred Bischoff, Oliver Sawodny. "On steady-state disturbance compensability for actuator placement in adaptive structures". In: at - Automatisierungstechnik 66 (8), pp. 591–603. 2018. doi: 10.1515/auto-2017-0099

[9] David Forster und Malte von Scheven. ”The Redundancy Matrix as a Performance Indicator for Structural Assessment“. In: Journal of Theoretical, Computational and Applied Mechanics, 13574. 2025. doi: 10.46298/jtcam.13574.