Numerical investigations of shape of the reflecting surface made of knitted mesh fabric being pulled on the curvilinear frame

Abstract

This paper presents the surface shaping numerical investigations results of truss space constructions mesh reflectors, such as antennas and calibration and adjustment satellites. Shape-generating structure of mentioned constructions adds up to set of triangular facets, made in the form of spatio-curvilinear bar frames, bearing reflecting knitted mesh fabric pulled on it. This work proposes the algorithm of calculation of step-by-step reflecting mesh pulling on the bearing frame’s bars process, using finite elements method. Numerical execution of the developed algorithm involves for resolving the linear elasticity theory first-type boundary value problem, which implies integration of elastic body equilibrium equations without taking into account mass forces when kinematic boundary conditions are given. Analyzing when having done numerical calculations, it's possible to determine what grade obtained shapes of reflecting surfaces are precise with, and to find possible for developing variants of the antenna structure, which would allow to obtain the reflector surface shape with required accuracy by using flexible cables as a part of shape-generating structure. Comparing results of numerical investigations with experimental data received using full-scaled model of spherical calibration and adjustment satellite shows satisfactory qualitative and quantitative matching of both results.