This study offers a theoretical solution for the neutral surface position of a space lightweight mirror employing two-axis bipod flexible mounts (TABFM) evenly distributed at three locations along the circumference. To maximize the surface shape accuracy of the mirror (SSAM) under the influence of radial gravity, it is typically necessary that the center of rotation of the TABFM coincides with the position of the neutral surface of the mirror (PNSM). Departing from the PNSM, the SSAM will be substantially deteriorated. In this paper, the compliance matrix of the TABFM utilized for space lightweight mirrors is initially solved. Subsequently, based on the compliance matrix, the analytical formulas and solution approaches for the PNSM under the action of 1g gravity are derived when the support structure of the mirror is symmetrically arranged horizontally and vertically. Additionally, a sensitivity analysis of the PNSM is also conducted. Finally, it is verified through the finite element simulation method. The results indicate that when the support structure of the mirror is uniformly distributed along the circumference and symmetrically arranged horizontally, the PNSM is solely related to the flexibility of the support structure, and the error between the theoretical calculation results and the finite element simulation results is merely 3.2‰; when the mirror support structure is uniformly distributed along the circumference and symmetrically arranged vertically, the PNSM is determined by the flexibility of the support structure and the mass characteristics of the mirror, and the error between the theoretical calculation results and the finite element simulation results is 2.1%. The proposed solution method of PNSM has been implemented in practical engineering projects. The method proposed in this paper can rapidly solve the PNSM and significantly enhance the efficiency and accuracy of integrated simulation optimization. Additionally, the method applies not only to the TABFM investigated in this paper but also to tripod mounts or other symmetric side support structures.
