Elastostatic and Aereolastic Problems Relating to Thin Wings of High Speed Airplanes

Citation

Fung, Yuan-cheng (1948) Elastostatic and Aereolastic Problems Relating to Thin Wings of High Speed Airplanes. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/JK8Q-RH35. https://resolver.caltech.edu/CaltechETD:etd-05222003-165709

Abstract

This report is concerned with the statics and dynamics of very thin wings of high speed airplanes. With the modern tendency towards sweepback, which is necessary for supersonic airplanes, the wing construction tend more and more to an ideal structure, hence for the static problem of this report, the wing is idealized to a thin cantilever elastic plate.

Part I gives a general formulation of the fundamental equations of deformation of thin elastic plates and the direct methods of solution. For small deflection of plates, the equations and boundary conditions are derived from the three-dimensional equations of elasticity developed in power series of the thickness of the plate. It is shown that the classical Poisson-Kirchhoff theory is coincident with the first approximation in this development. These equations are then transformed into oblique coordinates for treating problems concerning swept plates. Since the problem of the cantilever plate is very difficult to solve from the standpoint of biharmonic analysis, emphasis is laid on the direct methods of solution which lead to useful approximate solutions with desired accuracy. Section 1.21 discusses the relation between plate problems and equivalent variational problems. Section 1.22 contains a systematic review of the Rayleigh-Ritz method of relaxation of boundary conditions, including the Trefftz method as one instance.

Part II discusses the general aeroelastic problems of high speed airplanes. For airplanes accelerating or decelerating through the transonic region, the coefficients in the aeroelasticity equations are of transient nature. Such transient perturbations are new phenomena in aeronautics but are sufficiently important to warrant detailed investigation. A general mathematical treatment is given, though due to lack of aerodynamic data at present, no specific example is included. A general solution is obtained and this solution is expanded into a generalized power series which proves to be particularly useful when the transient perturbation is small. The present result includes the ordinary small perturbation theory for finite degrees of freedom as a particular case. Several results regarding small perturbations are given in section 2.6.

The next two parts give a detailed computation on the deflection of and stresses in cantilever plates. The deflection of rectangular cantilever plates is solved both by the Rayleigh-Ritz method and the method of relaxation of boundary conditions. For swept plates the Rayleigh-Ritz method is used. A theory of stress approximation without using the intermediate deflection function is developed in Part IV, and is applied to rectangular plates.

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