Optimal choice of design parameters of the umbrella-type antenna spoke to reach maximal bending stiffness

The paper is devoted to cross-section geometrical parameters optimization of thin-walled spokes of large-size, um- brella-type deployable satellite parabolic antennas with radial spokes. The spokes in the structures mentioned above must have maximal bending stiffness and minimal mass. Spokes with uniform thickness of walls both in the section and along their lengths are not optimal to achieve the maximal stiffness while keeping predetermined mass, because they have the same bending stiffness in any direction. In the given paper the authors suggest changing the shape of the spoke cross-section by using sections of different thicknesses. This would allow increasing the bending stiffness of each spoke in the perpendicular to the antenna surface direction while preserving the same mass of the complete structure. The thickness will be increased stepwise in the cross-sectional areas of the maximum distance from each other in the bend plane; in the remaining part of the section it will be reduced. The main objective of this paper is to obtain analytical dependences for assessment of the bending stiffness of the cross section of the umbrella-type antenna spoke with a stepwise change in its thickness. Formulas were obtained within the framework of the beam theory of bending. The obtained analytical dependencies were verified by numerical simulation in the finite element software Ansys. Verification of the obtained results by numerical simulation showed good convergence with theoretical conclusions. The formulas obtained in the paper make it possible to give practical recommendations for design of large deploy- able space antennas with improved parameters, namely maximum stiffness with minimum mass of the structure.