Incremental Potential Flow Based Membrane Wing Element

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Abstract
A new quadrilateral membrane wing element is presented that combines an incremental formulation of the elastic membrane problem with a vortex lattice formulation of the thin wing aerodynamic problem. The incremental formulation leads to an explicit/implicit velocity-stepping algorithm for solving the coupled aeroelastostatic membrane wing problem. The Stein-Hedgepeth wrinkle model is adopted as the constitutive relation for the membrane, which may develop slack or wrinkled regions. The element is shown to satisfy two limiting cases of the aeroelastic problem for which there are well-known analytic solutions. The algorithm is applied to two moderate aspect ratio membrane wing configurations with the second configuration being a model of a marine sail