Geometric Stiffness Effects on Data Recovery of an Idealized Mast/Blanket Model

The photovoltaic arrays for the international space station consist of a pre-tensioned blanket of solar collectors and a deployable mast. NASA uses the MSC/NASTRAN finite element program for modeling the dynamic response of the structure due to various loading conditions, such as plume impingement during shuttle docking. This finite element program uses the updated stiffness matrix (elastic plus geometric, or initial stress stiffness matrix) in determining the natural frequencies and mode shapes, as well as the dynamic response, of a pre-loaded structure. However, during the data recovery phase, when the moment and shear at the supports, and internal stresses are determined, geometric stiffness effects are neglected, and only the elastic stiffness is used in the calculation. The purpose of this study was to determine whether using the actual displacements, calculated based upon both elastic and geometric stiffness effects, would produce acceptable results in predicting shear and moment if the geometric stiffness effects were later omitted during data recovery. In this study, the PV array was idealized as a cantilever beam with an attached pre-tensioned cable. Static and dynamic analysis were performed, both using and neglecting the geometric stiffness matrix during data recovery. When considering the idealized mast/blanket model, neglecting the geometric stiffness contribution during data recovery led to a 32.2% difference in the vertical (shear) load at the fixed support, and an 8.8% difference in shear at the free end of the beam (compared to the inclusion of geometric stiffness effects in the analysis). The static analysis provided similar results and supported the \u27\u27reasonableness\u27\u27 of the dynamic analysis. Due to the large discrepancies in the predicted stresses which can ocur when geometric stiffness contributions are neglected during data recovery, it should be imperative that when a structure contains pre-loaded elements, the geometric stiffness effects must be fully considered both in the determination of the natural frequencies and mode shapes, as well as in the subsequent calculation of nodal reactions and stresses