Design and Optimization of Beam and Truss Structures Using Alternative Performance Indicators Based on the Redundancy Matrix

In structural optimization processes, a common goal is to limit deflections or stresses through topological changes, shape adaption or cross-sectional adjustments. Beyond these well-established performance indicators, alternative measures for the assessment of structures based on the redundancy matrix can be used in the design and optimization process. This contribution shows the extension of the redundancy calculation to three-dimensional beam structures in detail. Using the concept of redundancy for the design of structures, one goal is to homogeneously distribute redundancy within a structure in order to make an overall collapse due to failure of individual elements less likely. Furthermore, the sensitivity towards imperfections is quantified by the redundancy matrix, offering the opportunity to design connections of substructures, such that no constraint forces are introduced during the assembly process. Those two concepts are showcased exemplarily within this contribution. The method is embedded into a computational co-design framework, which allows for quick, interactive feedback on design changes to strengthen the interplay between the design and engineering process.