On the elastic membrane in a potential flow

Methods for the calculation of potential ßow around thin bodies are well known and can be found in several publications. According to these publications the vortex lattice method (VLM) combined with the quasicontinuous- method (QCM) is most e¤ective for membrane-like bodies with no aerodynamical thickness. The possible ßow around edges of a membrane causes singularities which are considered using a cosinespaced vortex lattice. The structural membrane analysis with the Þnite element method (FEM) is also well known and has been applied to several problems of engineering. If the same mesh is used for both methods it is easy to combine the QCM and the FEM. However, a cosine-spaced FE-mesh makes no sense because it is not FEM problem-orientated. Therefore, until now, equidistant or nearly equidistant vortex lattices have been used to calculate the interacting ßow and structure. They also cause unacceptable errors because they are not optimal for the VLM problem. This paper describes a new method to reduce the errors of combined calculations of ßow and structure. A FEM problem-orientated mesh out of improved Þnite elements is combined with a cosine-spaced vortex lattice. The method is called quasi-continuous-continuous (QCC) because the discrete forces of the VLM are transformed into a continuous membrane load. A set of numerical examples shows the excellent numerical performance of the QCC and the reduction of errors.