Form-finding design method for mesh reflector antennas considering the geometric nonlinearity of the truss

Abstract

Form-finding design serves as the crucial step towards attaining the desired electromagnetic performance of antennas, while laying the groundwork for subsequent design phases. To achieve an efficient and high-precision design of mesh antennas, a form-finding method considering the geometric nonlinearity of the truss has been proposed. In this approach, an investigation into the coupling relationship between the cable net and the truss is conducted, followed by a discussion on the deformation mechanism stemming from the geometric nonlinearity of the truss. Subsequently, a system equilibrium equation is established for the holistic design of mesh antennas, and an incremental equation, namely the tangent stiffness matrix, is further derived to enhance the iterative convergence rate and precision of the antenna’s transition from its initial state to the desired equilibrium state. On this basis, the sensitivity matrix of the antenna nodes regarding the force density vector is derived, and the functional relationship between the form-finding design objective and force density increment is established. The form-finding process is transformed into an easily solvable sequential quadratic programming function. Finally, the design accuracy and efficiency of the proposed method are verified through numerical examples.