A Unified Modeling and Analysis Strategy for Space Membrane Structures Based on IGA: Form Finding, Vibration Analysis with Pretension and Air Effects

Space membrane structures typically operate under tension, requiring a new geometric shape to be obtained through form-finding analysis, followed by vibration analysis based on the updated structure. Additionally, the impact of air on membrane vibration during ground modal testing cannot be ignored. In traditional approaches to membrane analysis, form finding and vibration analyses with pretension and air effects are conducted separately using various techniques (numerical methods or commercial software), making the process highly cumbersome. This paper introduces a unified modeling and analysis strategy within the framework of isogeometric analysis (IGA) to effectively address this challenge. First, non-uniform rational B-splines (NURBS), known for their natural high-order continuity, are employed to discretize the membrane structure. Combined with the dynamic relaxation method, efficient form-finding analysis of the membrane structure is conducted, ensuring a seamless integration between structural design and form finding. Subsequently, based on the new geometric shape, vibration analyses of space membrane structures considering pretension and air effects are performed by updating the stiffness matrix and introducing the added mass method. The proposed strategy leverages the precise modeling and efficient analysis capabilities of IGA and enables multi-demand analysis of space membrane structures using a unified model. The numerical examples validate the correctness and efficiency of the proposed strategy using benchmark cases. Additionally, the proposed strategy is applied to the multi-demand analysis of membrane antenna arrays.