Determining how loads are distributed in a structure has long been a way for engineers to ensure that the final product will work as intended. As components become more and more complicated so does this analysis. The advantages of quickly identifying critical features in a design are significant. By gaining this knowledge it is possible to explore the design space more thoroughly. This was previously done by collecting information over a long period of time and gradually build up the knowledge which can take several weeks or sometimes even months. The theory of the U* index as a numerical analysis method was formulated in 1986 by Takahashi [30] but due to the computational capabilities at the time there was no practical applications. It aims to give the same information compared to the current iterative process in a significantly faster way by calculating the relative stiffness. In its current form it can however be computationally heavy and has not yet seen any extended applications in the engineering sector. As the U* index is both an algorithm for calculating the load paths but also a broader theory of energy based identification of the stiffest route in a structure, it is referred to both as a method and a tool. In this thesis we initially set out to identify needs in the product development processfor a engineer team. Then we will investigate the capabilities of the U* index method, improve said capabilities by optimizing computation time and compatibility, establish a foundation for future development, and finally propose an integration of the tool into an advanced aero-engine development process. The main focus of this thesis is on the concept solutions phase as the needfinding indicated this phase to be in most need of improvement. Other applications of U* are mentioned but will not be examined in detail. In the concept solutions phase one would want to evaluate design features from a larger perspective to explore thedesign space. This can be done with U* by identifying which features are carrying the loads and how close the calculated path is to the optimal one. A possible application in optimization in the preliminary solution phase were also identified. In this case one can for example analyze the contour of the U* field and use U* sum to identify the relative load carrying contribution of certain regions. The initial state of the technology was determined to be at a technology readiness level (TRL) of 5 in the ModSim scale, meaning that the key elements have been demonstrated on a realistic problem. As the goal of applying the tool on real large models was achieved, the complete system level capabilities were demonstrated resulting in TRL 6 being reached at the end of the development. The more commonly used NASA version of TRL started out at TRL 3 which was reached with the proof of concept conducted by Ramesh [24]. According to these definitions the technology didn’t progress any further due to the specific definitions being primarily oriented towardshardware and the requirement for TRL 4 involved laboratory validation. As the TRL have been assessed with both versions, any potential future work has the option tochoose which method fit that particular work. The successful implementation of theinspection load method for calculating U∗ was critical in being able to compute thesolutions in reasonable time frame. There is however more room to optimize time byimplementing algorithms for better suited meshing and post processing. The tool is applicable on large components but the solutions still require a lot of time which reduces its usefulness in the early, time critical phase. The post-processing routines similarly take time and require extensive manual labor to determine the proper load path. This is also sub optimal for visualizing the load paths because it relies on assumptions. Future work should therefore aim to maximize the automation part of the post-processing. Further validation needs to be conducted on more complicated structures to ensure correlation between physical components and simulation. Furthermore, the quantifying of margins, uncertainties and sensitivities of the simulation is important to better understand the limitations of the tool.

Load transfer analysis deals with an important function of engineering structure, which is the ability of structure in transferring imposed loads to the supporting points. Although stress value has proved to be an efficient index for performing the failure analysis, the necessity of defining an index for evaluation of structure stiffness has led to the introduction of the U* index theory. The U* index characterizes the internal stiffness distributions, as an indicator of the load transfer in the structure. Although U* index theory have been proven to be useful in design, it is missing necessary steps toward becoming a mature theory for structural analysis. Firstly, the U* index theory needed to be examined and validated by experimental testing. Therefore, an experimental setup was proposed and tested, and U* index theory was validated through comparison of results. Secondly, a systematic comparison between the conventional stresses analysis and the U* index analysis was lacking. Such comparison was made for structural analyses of a vehicle component. The results, also compared to observations of experimental testing showed that in some cases, application of conventional stress analysis might be limited or less precise. Thirdly, design modification capability is a significant feature of the U* index theory, and it was necessary to demonstrate that real life problems can benefit from this potential. In this study, sample structures representing the components of multiple passengers carrying vehicles were selected and analyzed by U* index theory and design modifications were proposed and implemented on the structure. Lastly, the U* index theory should be applicable to different types of problems, including nonlinear domain. Hence, to remove the limitations of linear analysis that is a part of the original theory, an extension of U* index theory to the nonlinear domain was proposed and tested. In summary, U* index theory provides an understandable explanation of load transfer in the structure and provides a general awareness regarding structural performance. He presented work showed that the existing methods of structural analysis have limitations in certain aspects that can be overcome by combining the perspective of U* index analysis to the existing structural analysis paradigm. / February 2017