Solar deflection of thin-walled cylindrical, extendible structures

Abstract

An analytical expression is derived which describes the steady-state deflection of a long, thin, tubular structure with a locked overlapped cross section subjected to solar heating in a 0 g environment. By transforming the angular coordinate to correspond to the solar direction, it is possible to obtain a single expression which describes the circumferential temperature distribution. Thermal bending is found by closed form integration of the temperature-induced loading about the principal axes as dictated by overlap geometry. Maximum thermal bending is evaluated for various overlap angles as a function of dimensionless groups which include all thermal and geometric parameters. It is concluded that an optimum design is one which incorporates an overlap angle at 155°. The results are presented in graphical form suitable for engineering design, and a specific example is discussed. Nomenclature a = cross-sectional area of tube A = temperature parameter B — dimensionless parameter e = thermal coefficient of expansion E = Young's modulus of elasticity f(08) = function defined by Eq. (16) F = heat input function / = area moment of inertia k — thermal conductivity M = thermal bending moment r = element radius