Coupled deformation behavior investigation of laminated piezoelectric beam-membrane structures for umbrella-type membrane antennas

Umbrella-type membrane antenna integrated with the Macro Fiber Composite (MFC) is a kind of typical beam-membrane hybrid structures. These structures are widely applied in large-scale space exploration missions. Conventional finite element model faces the challenges of interface discontinuity and unstable convergence when simulating the large, coupled deformations. This manuscript presents a new Hybrid Element Model (HEM) employing the improved absolute nodal coordinate formulation. Firstly, the piezoelectric beam element and the thin shell element are formulated using the bicubic Hermite interpolation polynomial. This approach effectively captures the axial bending behavior of ribs as well as the deformation of films. Secondly, the coupled deformation criterion for hybrid structures is presented. This criterion guarantees continuity at the beam-membrane interface and achieves the coordination of coupled deformations. Additionally, the smoothness and continuity of stress at the beam-membrane interface are enhanced by improving the boundary constraint conditions of the membrane. Numerical analysis demonstrates that the proposed HEM method can accurately predict the coupled deformation behavior of beam-membrane hybrid structures under the piezoelectric effect. The HEM method achieves high convergence performance, and enhances computational efficiency as well.