Stress and fatigue constrained topology optimization

Sammanfattning: This thesis concerns structural optimization in conceptual design stages, for which constraints that are adapted to industrial requirements have been developed for topology optimization problems. The objective of the project has been to identify and solve problems that today prevent structural optimization from being used in a broader sense in the avionic industry; the main focus has been on stress and fatigue constraints in topology optimization.The thesis consists of two parts. The rst part gives an introduction to topology optimization and describes the developed methods for stress and fatigue constraints. In the second part, two papers are included, where the stress and fatigue constraints are evaluated, respectively.In the rst paper, a clustered approach is presented, where stress constraints are applied to stress clusters, rather than points on the structure. This allows for a trade-o between computational time and accuracy, as the number of clusters and thus constraints can be varied. Dierent approaches for how to sort stress evaluation points into clusters and how to update the clusters, such that the results are suciently accurate for conceptual designs, are developed and evaluated. The two-dimensional examples conrm the theoretical discussions and the designs that are obtained have managed to avoid large stress concentrations, even for problems with an initial stress singularity. Compared to the traditional stiness based designs, the stress constrained designs are considered to be closer to a nal design, which will decrease the total product development time.The second paper uses the methodology developed in the rst paper and applies it to high-cycle fatigue constraints. Using loads described by a variable load spectrum and material data from fatigue tests, the tensile principal stresses are constrained by a limit that is determined such that fatigue failure will not occur. In the examples, where the mass is minimized subjected to fatigue and static stress constraints, simple topologies are obtained and the structural parts are sized with respect to the critical fatigue stress and the yield limit. Stress concentrations are again avoided, for example by the creation of a radius around an internal corner. A comparison between static stress constraints based on the von Mises criterion and the highest tensile principal stresses is given and the examples clearly show the characteristics of the two formulations.