Approximate static aeroelastic analysis of composite wings

Purpose The purpose of this paper is to consider divergence of composite plate wings as well as slender wings with thin-walled cross-section of small-size airplanes. The main attention is paid to establishing of closed-form mathematical solutions for models of wings with coupling effects. Simplified solutions for calculating the divergence speed of wings with different geometry are established. Design/methodology/approach The wings are modeled as anisotropic plate elements and thin-walled beams with closed cross-section. Two-dimensional plate-like models are applied to analysis and design problems for wings of large aspect ratio. Findings At first, the equations of elastic deformation for anisotropic slender, plate-like wing with the large aspect ratio are studied. The principal consideration is delivered to the coupled torsion-bending effects. The influence of anisotropic tailoring on the critical divergence speed of the wing is examined in closed form. At second, the method is extended to study the behavior of the large aspect ratio, anisotropic wing with box-like wings. The static equations of the wing with box-like profile are derived using the theory of anisotropic thin-walled beams with closed cross-section. The solutions for forward-swept wing with box-like profiles are given in analytical formulas. The formulas for critical divergence speed demonstrate the dependency upon cross-sectional shape characteristics and anisotropic properties of the wing. Practical implications The simple, closed-form formulas for an estimation of critical static divergence are derived. The formulas are intended for use in designing of sport aircraft, gliders and small unmanned aircraft (drones). No complex analysis of airflow and advanced structural and aerodynamic models is necessary. The expression for chord length over the span of the wing allows for accounting a board class of wing shapes. Social implications The derived theory facilitates the use of composite materials for popular small-size aircraft, and particularly, for drones and gliders. Originality/value The closed-form solutions for thin-walled beams in steady gas flow are delivered in closed form. The explicit formulas for slender wings with variable chord and stiffness along the wing span are derived.