LAUSR

Abstract Form finding plays an essential role in the design of deployable mesh reflectors (DMRs), and it concerns their electromagnetic performance. However, classic form finding methods ignore the compatible deformation between cable networks and supporting structures. Even though the finite element method can be adopted to compensate the deviations caused by the compatible deformation, many iterations have to be involved and the effects are usually not satisfied. In this paper, an integrated form finding method considering the flexibility of the truss and hinges is proposed. Firstly, the rod of the truss is modeled by Euler–Bernoulli beam and the hinge is described by the flexible joint with six degree of freedoms (DOFs) to form the integrated element. These elements are assembled according to the topology of the truss to obtain the equilibrium equation of the truss. Secondly, the boundary conditions are applied to condense the DOFs of beam nodes, so that the rods, hinges and cable networks can be combined by adopting the corresponding consistency conditions, and then the equilibrium equation of the coupled model is established. Finally, the integrated form finding method is formed by incorporating the gradient based optimization method into the coupled model. This method is further applied to the form finding of the ring truss DMR, and the corresponding case studies are provided. The stiffness coefficients of three kinds of hinges in six DOFs are measured and utilized. The obtained design parameters are imported into ABAQUS to calculate the actually formed reflective surface, so as to verify the result. The form finding results are also compared with those in previous literature. The proposed method is proved to be effective in the form finding of DMRs, and the deviations of the form and force distribution of reflective surfaces caused by the compatible deformation are totally avoided.