Efficient aeroelastic beam modelling and the selection of a structural shape basis. (June 2019) - Howcroft, C.; Neild, S.A.; Lowenberg, M.H.; Cooper, J.E.
Abstract: This paper considers the selection of structural shape bases for the modelling of flexible beams using the nonlinear beam shapes formulation. The approach provides a low order geometrically nonlinear representation of a flexible beam using a kinematic description that is geometrically exact; a minimal state representation is achieved by projecting the problem onto a set of shape functions spanning the beam. Motivated by the requirements for the low-order modelling of aeroelastic systems, this study examines the practical requirements of applying these shape sets to a flexible wing problem. A number of candidate shape sets are presented: orthogonal and non-orthogonal, with and without load dependent boundary conditions. The efficiency with which this problem is solved is used to assess the performance of each candidate shape set and infer the common properties between the most efficient bases. For a system with a moderate number of states a fairly consistent performance is observed across all of the sets. For larger sized problems, orthogonality of the shape basis is required to ensure robustness and scalability. It is shown that for a generic basis set the necessary boundary conditions of the problem can be easily satisfied, furthermore any orthogonal properties of a chosen basis can be retained. This concept is extended to allow for the treatment of more complex configurations starting from a simple shape basis. Highlights: Satisfaction of natural boundary conditions not required in constructing an efficient representation. Orthogonality of base sets ensures robustness of formulation for problems over larger state sets. Set scaling may be used to satisfy the kinematic boundary conditions for generic starting bases. Orthogonality of the chosen base sets may be retained throughout the scaling process. More complex non-smooth configurations may be treated starting from a simple initial shape basis.