"The aims of this project are the advancement of methods for shape finding and optimization of adaptive structures as well as their application to the Stuttgart SmartShell. The key innovative aspect is a holistic system optimization of adaptive structures (as opposed to an a posteriori 'optimal' adaptation of initially passive structures). Consequently, the notion of optimization of system behavior via adaptation has to be clearly distinguished from optimization of an adaptive system as a whole. The potential for manipulation of a given structure via adaptation of forces, displacements and stiffness is an intrinsic system property, which has not been systematically investigated up to now. As a prototype of an adaptive thin-walled structure, the Stuttgart SmartShell offers the unique possibility to experimentally support and validate the newly developed methods." (source: DFG project description)
Form finding for adaptive structures
Shape finding or form finding in structural mechanics is known as an inverse problem, where the internal forces or stresses are prescribed while the shape to satisfy equilibrium is computed. Well-established form finding methods assume one shape-determining load case, which is usually the self-weight of the structure. Methods for form finding w.r.t. multiple load cases or adaptive systems are not sufficiently researched. This is one aim of research within this subproject are. Furthermore, the extension of existing form finding methods to holistic system finding methods is approached.
So far, a non-linear method based on the classical force density method was extended such, that shapes of adaptive spatial truss structures under multiple static loads may be computed taking additional design constraints into account.
Regarding the extension to system finding methods the so-called disturbance-compensability matrix was developed in cooperation with control engineers from Institute of System Dynamics (ISYS) of University of Stuttgart (Wagner et al. (2018)). This matrix is a special Gramian matrix independent of load cases that describes the system inherent properties of a structure to be adapted w.r.t. its states (like forces or displacemets). On this basis, a greedy algorithm for actuator placement in adaptive truss structures is developed. Studies on exemplary truss structures revealed that the optimal compensability of internal forces is reached, if the number of serial actuators is equal to the degree of statical indeterminacy of the structure n and all statical indeterminate structural parts are adapted. Additional actuators does not have any more further effect on the compensability, because the image space of the corresponding disturbance-compensability matrix is of dimension n (Wagner et al. (2018)).
Optimization methods for adaptive systems
Regarding analytical and numerical methods a sharp distinction between form finding and shape optimization is not possible. Form finding tasks may be formulated as mathematical optimization problems. Within a cooperation with the Institute Engineering and Numerical Mechanics (ITM) of University of Stuttgart a parametric model order reduction method for geometrically parametrized systems was developed and applied for efficient shape optimization of an adaptive bridge structure (Fröhlich et al. (2019)).
A crucial hypothesis in optimized design of adaptive structures is the following: The optimization of an adaptive structures is principally superior to the adaptation of a priorly optimized passive structure. This hypothesis was verified by means of analytical investigations and numerical studies (Geiger et al. (IFAC, 2020)).
Moreover, design and optimization strategies concerning mass saving potential were evolved (Geiger et al. (BB14, 2020); Geiger et al. (Frontiers, 2020)). Significant mass savings may be realised if displacement constraints are decisive for the structural design (so-called stiffness-governed problems).
Criteria for system optimization of adaptive structures
Within this subproject area the advancement of criteria for optimal shapes and topologies of adaptive structures is focused. In the sense of an holistic system optimization the adaptive structure is considered as an entire system consisting of structure, sensors, and actuators.
So far, approaches from control engineering are focused and the above-mentioned disturbance-compensability matrix was studied. A meaningful interpretation of modal properties of the matrix from structural mechanics as well as from control engineering point of view was found in order to gain a deeper understanding of the developed actuator placement algorithm (Wagner et al. (2019)).
Furthermore, the redundancy concept (von Scheven et al. (2020); Geiger et al. (BB14, 2020)) was focused. Based on the analysis of algebraic spaces of redundancy matrices, scalar-valued performance criteria for the adaptability of force states under static behaviour were derived. Afterwards, in a cooperation with the Institute of Computational Design and Construction (ICD) of University of Stuttgart, such criteria were implemented into an agent-based system for explorative generation of adaptive truss structures.
Teilprojekt A04 - Formfindung, Strukturoptimierung, Systemoptimierung adaptiver Tragwerke
German Research Foundation (DFG), Collaborative Research Centre SFB 1244 "Adaptive Hüllen und Strukturen für die gebaute Umwelt von morgen", GEPRIS project number 324661605
Institute for Lightweight Structures and Conceptual Design (ILEK), University of Stuttgart
- Geiger, F., Gade, J., von Scheven, M., & Bischoff, M. (2020). Anwendung der Redundanzmatrix bei der Bewertung adaptiver Strukturen. Manfred Bischoff, Malte von Scheven, Bastian Oesterle (Hrsg.) Berichte der Fachtagung Baustatik – Baupraxis 14, 23. und 24. März 2020, Universität Stuttgart, 119–128. https://doi.org/10.18419/opus-10762
- Fröhlich, B., Gade, J., Geiger, F., Bischoff, M., & Eberhard, P. (2019). Geometric element parameterization and parametric model order reduction in finite element based shape optimization. Computational Mechanics, 63, 853–868. https://doi.org/10.1007/s00466-018-1626-1
- Wagner, J. L., Gade, J., Heidingsfeld, M., Geiger, F., von Scheven, M., Böhm, M., Bischoff, M., & Sawodny, O. (2018). On steady-state disturbance compensability for actuator placement in adaptive structures. at – Automatisierungstechnik, 66, 591–603. https://doi.org/10.1515/auto-2017-0099