Deflection and Stress Patterns in Plate-Type Structures, Theory Vs. Test Results

Abstract

V = potential energy \W = deflection matrix x = variable distance along the chord y = variable distance along the span {(f>j} = functions of deflection (j = 0, 1, and 2) u = Poisson's ratio (constant) a = principal stress <jx = chordwise stress oy = spanwise stress TXV = shear stress This report presents a practical analysis of the deflection and stress distribution throughout a plate-type structure with variable stiffness, loading, and boundary conditions. I ts application is to aircraft and missile wing and fin structural design, and the determination of the deflected shape of an airfoil surface under aerodynamic loading. The basic assumption used for the approximation of the rigorous theory is tha t of idealizing deflections. In this manner, the chordwise deflection a t any spanwise station is expressed in the form of a parabolic equation, where the coefficients are unknown functions of the spanwise stations. By utilizing the idealization, each spanwise station has three degrees of freedom tha t must be determined. This analysis allows the theoretical matrix plate equations to be programed easily on a high-speed digital computer; once programed, a practical wing may be designed by two or three stress analysts in a short period of time. The particular theory developed in this paper is for application to full-depth honeycomb construction, which is very efficient weightwise for a thin low-aspect-ratio airfoil surface. The problems presented are for airfoil surfaces attached to the side of a shell-type structure with full and partial root support. Comparisons of root support are shown in order to demonstrate the variation of deflection and stress distribution. In order to establish the validity of this analysis, and to verify that the results obtained may be applied to a plate-type structure, a test program was undertaken. The theory was then applied to two typical problems, and an experimental program was conducted. The results were then compared.