Statistical Sensitivity Analysis of Lattice Space Structures

This paper presents a statistical sensitivity analysis for shape distortions of space structures. The approach is based on a statistical shape‐distortion analysis on the structural errors and an adjoint method of sensitivity analysis. The statistical shape‐distortion analysis allows the stochastic errors to be represented by member‐length tolerances. The sensitivity analysis is performed to predict the effects of member‐length errors for lattice space antennas on the surface accuracy. The formulas presented in this paper give an effective approach to predict the effects of member‐length errors on the shape distortions, to obtain effective structural elements to correct the shape distortions, and to design tolerance errors of the structural elements. Numerical examples for statically determinate and indeterminate two‐dimensional truss beams have been demonstrated to identify the members contributing most to the errors. These results show that the errors of the longitudinal elements of the structure are important for designing accurate truss structures. Moreover, the validity and effectiveness of the present approach have been investigated.