Strain-Based Shape Estimation for Annular Plates

Large flexible structures are used in many space applications, for example, satellite communication antennae, space robotic systems, and space station, etc. The flexibility of these large space structures results in problems of structure shape deformation and vibration, etc. In recent years, active shape control is developed to improve the performance of these flexible space structures. However, it is difficult to measure the surface shape of large flexible space structures in space environment. In this paper, a shape estimation method was developed to determine deflection of annular structures under arbitrary loading and boundary conditions. The shape estimation method utilizes strain information from strain gage sensors mounted on the structure. The strain field is calculated using polar components of stress in terms of Airy’s stress function. The coefficients of each function are determined based on the relationship of strain, displacement, and strain compatibility. The strain field is constructed by least squares smoothing procedure. This shape estimation method was verified by the numerical method, finite element and the experimental results. The results show that the shape estimation method can be used to determine deformation shape of the annular plate for active shape control of flexible structures.