In the presented work, we have developed a method to analyse the interaction between the wind and membrane structures. The complex behaviour of light weighted membrane structures can induce dynamic and wind effects, so this requires an appropriate method to analyse the structure. When the deformation of membrane structures is large, it becomes necessary to consider the interaction between wind flow and membrane. This interaction leads to aeroelastic problems.
The necessary properties to be considered for the aeroelastic coupled problem are considered and presented. The major focus of the thesis is to simulate the geometric non-linear behaviour of the membrane structures when subjected to wind loading. To derive the initial equilibrium shape, the method of form finding is applied. To properly simulate the wind flow around the structure, existing research regarding wind tunnel testing of a hemispherical air dome model is used. First, hemispherical model similar to existing research was made to verify the boundary conditions. The results are compared to the wind-tunnel testing results to get proper boundary conditions in Computational Fluid Dynamics models. In order to keep the simulation simple, the wind velocity is considered constant with height and constant wind flow with respect to time.
Partitioned analysis is used to simulate the physics behind the wind-membrane interaction simulation. By using this method, the multi-physics problem is separated into individual fields. Considering the wind-membrane interaction, the problem is separated into fluid domain and structural domain.
The structural and fluid domain mechanics are discussed in detail. For the single field solvers, methods are introduced based on the fundamentals. Finite Element method is used for the form-finding as well as numerical simulation of the structural field and SOFiSTiK software is used. For the fluid simulation, ANSYS CFX is used.
The strong physical coupling is done between the fluid and the structural domain. For this, the partitioned coupling simulation is used. The requirements and methods for the partitioned analysis are presented as well. For the coupling of separate solvers, a central coupling tool is made using Grasshopper. The transfer of coupling data such as displacement and wind pressure on the membrane structure is done using the developed coupling tool. In the development of this coupling method using Grasshopper, Python programming language is used. The developed method was used in iterations to analyse the effect of geometric non-linearity.
In order to make the developed method reusable for the air-supported membrane structures, the whole process is made parametric using grasshopper. This enables us to analyse the membrane structures with known base shape, internal air pressure. Ultimately this method can be used to analyse the effect of geometric non-linearity on membrane structures when subjected to wind loading. To show the use case of developed method, two different models are developed to analyse the fluid structure interaction. First model has been considered with a circular base shape and the second one has been considered with a square base shape. In order to analyse the effect of geometric non-linearity on these structures, the results such as maximum wind pressure on the membrane structure and maximum structural displacement are compared to the results without considering the geometric non-linearity.
Moreover, wind variation analysis is done to analyse the extent to which geometric non-linearity is dependent on the wind speed. Similarly, size variation analysis is also done to analyse the extent to which geometric non-linearity is dependent on the structure size, keeping the wind velocity constant.

In the design of steel structures, optimisation methods promise cheap, light and sustainable structures. However, the resulting designs tend to have a high diversity of profiles, making them unbuildable. Furthermore, the optimisation problem is mathematically complex, leading to a long and potentially unsolvable optimisation process. Grouping methods solve both issues by finding the optimum solution, for which the number of distinct profiles is limited. Multiple grouping methods exist in literature, and it is not known which is the best: the methods have not been applied on the same problems, and the computational effort has not been compared. This gap in literature leads to the following question: “Which method for grouping can find the lightest and cheapest steel structure with minimal computational effort?” To answer this question, a comparison of the existing grouping methods is made on their theoretical and numerical performance. The theoretical comparison comprises the size and properties of the search space, and the number of additional calculations. The numerical comparison consists of weight optimisation of eight benchmark problems. For each structure and method, the weight of the solution and corresponding computational effort is evaluated. Manually grouping of members, which is the most popular grouping method, relies on the engineer’s expertise and rules of thumb. This method requires no additional calculations but in general fails to find the optimum grouping for a light or cheap structure. Other existing methods include the geometry, axial force distribution or an ungrouped result in their grouping process, or adapt the optimisation problem. Of these methods, only the cardinality constraints method is guaranteed to potentially find the lightest grouped design, while reducing the search space for a small number of groups. However, it creates many local optima, which increases the complexity of the search space. In the aim of finding a grouping method which creates a simple and small search space and has low computational effort, the fully stressed combinatorial search method is proposed. In this method, the grouping is found by a combinatorial search, which evaluates the estimated weight or costs of a restricted set of groupings based on the weight per unit length of the members of a fully stressed design. Then, optimisation of a small and simple search space finds the corresponding optimum profiles. These steps are repeated, in which the fully stressed design uses the result of the previous optimisation as its reference design. The loop repeats until the grouping is unchanged, or the result diverges. In all numerical experiments, the new method gave results with a low weight, while it kept the computational effort to an acceptable level. It gave the lightest design for four out of eight problems and showed high certainty for converging to the lightest design in two problems. For the other two problems it performed second best. Conclusively, this method is the best available grouping method for steel structural optimisation. In case of cost optimisation, the new grouping method can efficiently find the optimum design including the optimum number of groups; the new method converges to cheaper design with less computations than in the case no grouping is applied. For a real-life case-study, the costs of a design were reduced with 7.3% compared to a manually grouped design and with 19.6% compared to the conventional design process. I suggest that further research focusses on further development of the new grouping method as proposed improvements can be made on the initial design, and the number of computations in the combinatorial search and fully stressed design. Moreover, the effectiveness of a suggested simplification of the new method should be investigated. This would allow application for engineers who are not able to apply a mathematical optimisation method. For practical application, incorporation of building codes and cost functions with a well-defined scope are desired. Finally, utilisation of the grouping methods in other applications is possible, but the performance of the methods should be evaluated per application.