On the Deflexion of Anisotropic Structural Composite Aerodynamic Components

This paper presents closed form solutions to the classical beam elasticity differential equation in order to effectively model the displacement of standard aerodynamic geometries used throughout a number of industries. The models assume that the components are constructed from in-plane generally anisotropic (though shown to be quasi-isotropic) composite materials. Exact solutions for the displacement and strains for elliptical and FX66-S-196 and NACA 63-621 aerofoil approximations thin wall composite material shell structures, with and without a stiffening rib (shear-web), are presented for the first time. Each of the models developed is rigorously validated via numerical (Runge-Kutta) solutions of an identical differential equation used to derive the analytical models presented. The resulting calculated displacement and material strain fields are shown to be in excellent agreement with simulations using the ANSYS and CATIA commercial finite element (FE) codes as well as experimental data evident in the literature. One major implication of the theoretical treatment is that these solutions can now be used in design codes to limit the required displacement and strains in similar components used in the aerospace and most notably renewable energy sectors. 1. Introduction Currently there is great deal of interest in the design of structurally efficient aerodynamic structures constructed of advanced composite materials. In the aerospace sector these are defined as a number of chemically distinct materials being macroscopically bonded with the resultant amalgamation being superior than original chemically distinct constituents [1]. The emphasis in the renewable and aerospace communities is to embed a strong (though usually brittle) ceramic material such as glass or carbon fibre in a polymeric material such as epoxy or more recently the biodegradable polypropylene [2]. The resulting composite material is a heterogeneous anisotropic material with a reality high strength-to-weight ratio. The consequence is that the polymeric material is made a couple of orders of magnitude stronger in addition to significantly increasing the displacement at failure when compared to the original ceramics employed as the reinforcement. Consequently, there has been much development of manufacturing processes in order to produce components such as wind turbine blades from these rapidly becoming inexpensive materials. Since the macroscopic bonding results in a heterogeneous more flexible material then the conventional assumptions of material failure tend to be inappropriate. It is