Kinetic heating effect on thin solid wings of finite aspect ratio

• Main Author: Mair, Barrie
• Published: Imperial College London 1968
• Subjects: 530.4
• Online Access: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.623084

In this thesis, some problems concerned with the large deflections of thin solid wings are investigated. First, an infinite strip of double wedge section subjected to spanwise bending, torsion and thermagradients is considered. Lateral deflections, stress resultants and stability boundaries are evaluated by a semi-exact process, in which numerical techniques are employed to avoid complicated integrations. The results agree well with those obtained using approximate polynomial expansions in the "small" large deflection regime, and also show close agreement with the results available for similar sections, like the biconvex wing. The second problem considered is that of the single wedge, infinite span wing under a pure spanwise bending moment, the analysis following directly from that of the double wedge. Difficulties arising from the unsymmetric section are overcome by a suitable definition of axes. To cater for sections not amenable to the analytic approach, a finite difference method is evolved in part three. The two previous problems are considered as examples, and the errors are found to be less than 1%. Finally, the practical wing problem of a cantilevered plate of finite aspect ratio, subjected to pressure and thermal loadings, is investigated. For simplicity, the example chosen is a square plate of constant thickness. The technique devised is shown to operate over the full region bounded by the two asymptotic solutions given by "small deflection" and "inextensional" theories. Based on the asymptotic formula, the accuracy of the method is estimated to be better than 1.5%. However, the governing differential equations of Von Karman are only valid under certain assumptions which do not hold for very large deflections, such as the approximate expression for curvature. It is shown that for the largest load considered, the error introduced in the curvature expression is 0(5%). Hence, above this value of loading parameter, the governing equations are seriously in error.