High Precision Shape Design Method For Space Deployable Mesh Antenna

Ring truss deployable mesh reflector antenna has been widely used in the fields of radar,communication and radio astronomy for its high expansion ratio,small mass-diameter ratio,and reliable deployment characteristics.As the boundary of electromagnetic fields,high precision surface is the key requirement for the antenna to complete its predetermined task.In this thesis,the high-precision shape design issues for ring truss deployable mesh reflector antenna is systematically studied.The main contributions of this thesis can be summarized as follows:1.The geometric optimization design for the reflecting surface with the goal of minimizing the faceting deviation is studied in this thesis.The relationship between the faceting deviation of the reflector and its projected geometry on the aperture plane is derived.The formula to calculate the faceting deviation by the projected side lengths of the reflector facets is given,and the fast calculation of the faceting deviation is realized.A modeling method for reflecting surface based on force density method is proposed,which avoids dealing with the complex node position constraints.The geometric optimization design model is established,by taking the force density as the design variable,the minimum faceting deviation as the goal,and the antenna aperture as the constraint,respectively.The feasibility and effectiveness of the design method is verified by numerical examples.2.A design method of quadratic curve reflecting surface is proposed in this thesis which comprehensively considers the effective aperture of the antenna and the uniformity of the spliced facets.Firstly,a series of quadratic curves that satisfy specific equations are generated in the ellipse intersection plane.Then,the dynamic key node optimization adjustment method is used to solve the problem of non-intersecting quadratic curves and to generate the plane mesh.Finally,the nodes are projected onto the paraboloid to obtain the final reflecting surface.Numerical results show that the quadratic curve mesh reflecting surface can obtain a larger effective aperture while maintaining better tension uniformity.3.The electromechanical coupling design method for reflecting surface is studied in this thesis.Firstly,the fast calculation of the antenna scattering fields is realized by using the Gordon formula to convert the integral operation of the scattering field of the mesh reflector into a linear operation.Then,based on Delaunay triangulation and centroid Voronoi diagram,electromagnetic calculation grids with uniform size are generated,which reduces the number of integral grids and further improves the efficiency of electromechanical coupling optimization design.Finally,the electromechanical coupling optimization model is established and used to design the mesh reflector.Numerical results show that the electromechanical coupling design method for reflecting surface can relax the requirement of surface accuracy,and has certain application potential and value in reducing the structural complexity of the mesh antenna.4.The pretension optimization design method for cable-net structure which can take into considering the deformation of the support is studied in this thesis.Firstly,the deformation analysis of the cable net structure with flexible frame is carried out by combining the linear finite method and the force density method,which avoids the nonlinear solution and improves the efficiency of the pretension optimization.Then,an optimization model is established to optimally solve the pretension of the cable net structure,and the cable length is choosing as the goal to take into account the influence of the rigid body displacement of the nodes,which exploding the solution domain.Numerical results show that the proposed design method can achieve high design accuracy and significantly improve the mechanical properties of the support,and thus has potential engineering value.5.The shape adjustment method for mesh reflector surface considering the data uncertainty is studied in this thesis.Firstly,the multi-stable states and precision jump phenomena existing in the deployable structure are studied,which are introduced into the adjustment model as the boundary condition uncertainty lately.Then,the shape adjustment model is established by equating various uncertain data as the uncertainty of cable pretension.Subsequently,aiming at the time-consuming problem existing in the analysis of uncertain structures,the LS-SVM model is introduced to establish the mapping relationship between the deformation of the reflector surface nodes and the adjustment amount of adjust cables.Finally,the optimal adjustment amount is obtained by numerical optimization solution,and the case studied is carried out.