Julian Mrochen: Entwicklung mathematischer Optimierungsmodelle für adaptive Stabwerkstrukturen (2026, dissertation)

Increasing demands for resource efficiency, structural performance, and the adaptability of technical systems are leading to a growing need for systematically designed truss structures. Particularly in the design of truss structures, the early use of optimization approaches offers the potential to save material in a targeted manner and to efficiently tap into structural performance reserves. In engineering practice, however, design is often based on simplified assumptions and subsequent adjustments, resulting in insufficient utilization of the available degrees of freedom in the design space. This can lead to oversized or structurally inefficient solutions and limits the achievable resource efficiency.

This thesis develops optimization approaches for the design of truss structures under practical constraints with the goal of systematically designing structurally stable and material-efficient structures. To this end, mathematical models are formulated that minimize material usage while simultaneously accounting for equilibrium and strength conditions to ensure mechanically robust structures. The developed approaches aim to ensure the stability of the truss structures already during the optimization process, thereby enabling a consistent and reliable structural design. Load-bearing structures for bending tools are considered as an application example, where high mechanical requirements and resource-efficient design are particularly relevant. Through systematic modeling, different boundary conditions and application scenarios can be represented within a unified optimization framework. A novel aspect of this work is the extension of the optimization models to include movable structural elements. These extensions should be understood as conceptual approaches and serve to demonstrate the potential of movable structures. By specifically allowing relative movements of individual nodes or substructures, new possibilities for the functional adaptation of truss structures are opened up. This thesis illustrates, through examples, which additional degrees of freedom and design options can be achieved through movable structures, thereby laying the foundation for further investigations into adaptive and functionally integrated concepts.