Accuracy analysis and form-finding design of uncertain mesh reflectors based on interval force density method

Mesh reflectors are uncertain structures because of the existing errors of dimension and material in the procedure of design and manufacture. These uncertainties have significant impacts on the mechanical and electrical properties, which must be considered during the design phase. Three directly related factors of cable uncertainties in mesh reflectors are considered in this paper, including the initial length, cross-sectional area, and elastic modulus. The analytical relationship between the cable uncertainties and the surface accuracy of mesh reflectors is deduced by interval analysis, and an interval force density method is thus proposed. First, this method is used to analyze the influence of the cable uncertainties on the surface accuracy. Then it is applied into the form-finding optimization of uncertain mesh reflectors to minimize the influence of cable uncertainties on the surface accuracy. Three kinds of cable nets of mesh reflectors are illustrated to analyze the influence of the cable uncertainties on the surface accuracy, and the mesh reflectors with high surface accuracy are obtained by the proposed method. Finally, the influences of both the design values and deviation amplitudes of cable uncertainties on the surface accuracy are revealed.