An aeroelastic model for the analysis of membrane wings and its application to yacht sails and Pteranodon ingens

Abstract

This thesis describes a method used for the aerodynamic and structural analysis of thin, elastic membrane wings and the techniques employed to couple these methods to develop an aeroelastic model. Through the development of an aeroelastic model and its application to appropriate examples, the aim of this study is to provide an improved understanding of the aeroelastic behaviour of membrane wings. A potential flow aerodynamics analysis is performed using a low-order panel method which provides the loading given the wing shape. The structural mechanics analysis is performed using a non-linear finite element analysis and provides the wing shape given the applied loading. The aerodynamic and structural analyses are coupled using a novel approach in which representations of the wing shape, mean velocity distribution, and potential jump are employed to permit interpolation of data. These representations are generated using the least squares method of modelling data. This approach facilitates the coupling of the two independent numerical schemes and results in an iterative model for the aeroelastic analysis of three-dimensional membrane wings. The dependence of the resulting aeroelastic model on the number of aerodynamic panels and structural finite elements used to represent the wing is demonstrated by application of the aeroelastic model to a simple triangular membrane wing. The convergence with increasing number of iterations is also demonstrated for the same triangular wing. The verification of the accuracy of the aeroelastic model is established by comparison of the results with those of previous authors for two test wings, with excellent agreement achieved for both cases. Aeroelastic investigations are performed for a series of wings that are analogous to idealised Litemational America’s Cup Class (LACC) yacht mainsails. The tests are performed over a range of aeroelastic numbers (a non-dimensional ratio of the elastic stiffness to the applied load) and angles of attack. Furthermore, the amount of initial camber, twist, and the aspect ratio are varied in order to determine what effects that these parameters have on the aeroelastic behaviour of membrane wings. The aeroelastic model is also applied to the analysis of the gliding flight of Pteranodon ingens, a large Cretaceous Pterodactyloid pterosaur. Four basic configurations are investigated, based upon the reconstruction of Bramwell and Whitfield [1974]. Tests are performed over a range of aeroelastic numbers, angles of attack, and geometry conditions. Upon variation of the camber and twist distribution, both unstable and stable configurations can be generated. It is illustrated that for unstable configurations Pteranodon ingens could vary its flight speed and achieve controlled flight by flexion and extension of the elbow and knuckle joints. The forces resulting from the aerodynamic loading applied to the bone structure are investigated and are shown to exceed the strength of the wing structure particularly in the region near the wing tips. This is most likely due to inaccuracies in the modelling of the geometry of the wing but may also be attributed to underestimates of the bone strength. It is also illustrated that the fibres present in the wings of pterosaurs do not align with the directions of the principal stresses and could not therefore act as believed in some previous studies. Here it is suggested that the purpose of the fibres in the wings of pterosaurs are in fact similar to that of the battens of yacht sails. Fi this manner they maintain structural integrity by allowing the wing membrane to carry compressive stresses and prevent wrinkling from occurring.