Stress compensation method for spatial tension membranes and free vibration analysis

Flexible solar arrays and membrane antennas, as typical aerospace structures utilizing tensioned membranes, are highly sensitive to stress variations and prone to wrinkling under compressive loads. To improve the accuracy of analytical stress field modeling, a stress compensation approach based on the principle of superposition is proposed for the free vibration analysis of corner-tensioned membranes. A radial stress distribution model induced by a concentrated force was first employed to construct the initial stress field. Considering the free-boundary characteristics of corner-tensioned membranes, a virtual boundary loading scheme was introduced to compensate the initial stress by applying external loads equal in magnitude and opposite in direction to the normal boundary stress. A vibration model of a square tensioned membrane was developed by incorporating geometric stiffness, mesh generation strategies, and the effect of added air mass. The effectiveness of the proposed method was verified through comparison with finite element simulations and NASA-released experimental data. The calculated first and second principal stresses at the membrane center showed relative errors of 0.93 and 2.15, respectively, when compared to finite element references. For modal analysis, the theoretical first natural frequency deviated by only 4.6 from experimental results, while the fifth mode exhibited a deviation of 27.7, confirming the method's effectiveness in predicting multiple vibration modes with good accuracy. The proposed stress compensation method accurately reconstructs a physically realistic stress field with smooth distribution and natural boundary transitions. It significantly improves the precision of modal predictions and shows strong potential for engineering applications. The method offers a reliable theoretical basis and practical tool for the design and dynamic analysis of flexible aerospace membrane structures.