Membrane structures are vulnerable to ponding due to their large deformation characteristic. The ponding on membrane structures is usually caused by rainfall on an already deformed structure due to a seeding event such as snow accumulation. This paper discusses two monolithic methods and a partitioned method for determining the static deformation of the membrane structure due to a given volume of ponding water. The monolithic methods involve simultaneously solving the structural equations and the fluid equations under static conditions, to obtain the structural deformation. The partitioned method on the other hand involves external coupling iterations involving a structural solver and volume conserving solver, where the volume conserving solver is responsible for updating the free surface to maintain a given volume of water. The discussed methods are compared in terms of robustness and computing time. It was found that the monolithic methods were computationally efficient. However, the partitioned method-apart from being modular-was found to be more robust with quasi-Newton convergence accelerators.
In 2011, during the Pukkelpop festival held in Kiewit (Belgium), the sudden development of a storm resulted in strong wind gusts that led to extensive damage to the festival tents [1]. During this event, there was also heavy rainfall which caused ponding on the membrane structures. We believe one possible mechanism that resulted in the damage to the tents is the large vertical oscillation of the water mass with the membrane, excited by the fluctuating wind loads. This can easily be seen in the available video footages. The primary motivation of the current work is to simulate such a phenomenon. This requires unsteady fluid-structure interaction (FSI) simulation involving the wind, ponding water, and a membrane structure. In previous work [2], we developed methods for determining the initial condition of membrane structure with ponding for the unsteady FSI simulation, where the developed methods were used to calculate the static deformation of membrane structures under ponding loads.In the present work, we propose a novel coupling strategy to solve such problems, where the wind, water, and membrane are simulated using three different solvers. The simulation of the wind is carried out by an OpenFOAM incompressible solver with large eddy simulation (wind solver), while for modeling the movement of water on the membrane an OpenFOAM volume of fluid solver (VoF) is used (water solver), and the structural solver with membrane elements in KratosMultiphysics is employed for modeling the membrane structure (structural solver).The coupling strategy couples the structural solver in parallel with the wind and the water solver. This means that in the partitioned simulation, the structural solver receives tractions from the wind and water solvers, which are added and applied to the structure. On the other hand, the wind and the water solver receive displacement from the structural solver, used for updating the fluid-structure interface. The main assumption in this strategy is that the interaction between the water and the wind is not significant compared to the interaction between the two fluids and the structure. The results from this strategy are compared with the reference simulation, where the two fluids are simulated together in a VoF solver, which is coupled with the structural solver.
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