Form-Finding of Large Deployable Mesh Reflectors with Elastic Deformations of Supporting Structures

摘要

Large Deployable Mesh Reflectors (DMRs) are widely used in development of space antennas for signal transmission purposes. In design of a DMR, high surface accuracy is required to meet operating frequency requirements and it depends on the positions of the nodes of the front cable net that form a reflecting surface. Therefore, maintaining cable net nodes in desired positions is essentially important to high surface accuracy and high performance of a DMR. In traditional form-finding for a DMR, the elastic deformation of the supporting structure, which has significant influence on the nodal positions of the front cable net, is often neglected. This ignorance of the deformation of the supporting structure does not warrant the desired surface accuracy of the DMR. In this paper, to address the above-mentioned issue, a new form-finding method is proposed, which considers the elastic deformation of the supporting structure in a DMR design. In the proposed method, a combined structure model that consists of two cable nets and a supporting structure is developed and the equilibrium equations at all the nodes are established. With the combined model and equilibrium equations, the nodal positions and the lengths of all the elements of the DMR are simultaneously determined. Different from traditional methods, the new form-finding method treats the boundary nodes of the cable nets as movable ones due to the elastic deformation of the supporting structure. As such, deviations in the nodal positions caused by the deformation of the supporting structure can be eliminated, assuring high surface accuracy in a DMR design process. The proposed method is applicable for both center-feed and offset-feed DMRs with symmetric and asymmetric rear cable nets.