Quasi-static unfolding mechanics of a creased membrane based on a finite deformation crease–beam model

A Review on the Development of Spaceborne Membrane Antennas

“…Murphey [108] developed array beam models with triangular/rectangular patterns and sine/linear shapes, to study the random creases on deployable surfaces. Other investigations can be found on the deformation of stretching membranes with creases using the beam model [109][110][111][112], large deformation, crease rotational stiffness, and hinged beam connection model.…”

Deployment and surface accuracy of regularly creased membranes

“…The importance of modelling both the crease and panel elastic responses showed the contribution of each mechanism during deployment, and highlighted the existence of a characteristic length scale below which the membrane deformation can be neglected, and the mechanical response can be approximated by a rigid-folded mechanism [21]. Experimental studies on different materials have shown a linear moment-angle relationship at the crease, which can be modelled as a rotational spring with constant stiffness [21][22][23]. Its constitutive behaviour and elastic contribution were included in a nonlinear beam framework aimed at obtaining the mechanical response of membranes with a single crease [23][24][25].…”

“…Experimental studies on different materials have shown a linear moment-angle relationship at the crease, which can be modelled as a rotational spring with constant stiffness [21][22][23]. Its constitutive behaviour and elastic contribution were included in a nonlinear beam framework aimed at obtaining the mechanical response of membranes with a single crease [23][24][25]. Recent works have improved the fold characterization by analysing the formation [22] and local response [26] of folds, their inelastic behaviour [27] and the viscoelastic effects on the initial opening angle [28].…”

“…The one-dimensional finite rotation crease-beam mathematical model, which is also capable of predicting the thin film surface accuracy during unfolding, is numerically and experimentally validated through tension tests performed with 2D and 3D digital image correlation. Furthermore, previous studies [21,23] characterized the contributions of panel bending and crease opening through a linear analysis and showed that a single parameter could describe the primary unfolding mechanism. In this work, by considering the energy contributions obtained from a fully nonlinear analysis, we show that two dimensionless parameters are required to capture the interaction between membrane and crease elasticities during deployment, offering tools to evaluate them.…”

Simulation of membrane deployment accounting for the nonlinear crease effect based on absolute nodal coordinate formulation

“…Furuya et al [9] treated the uniformly loaded Z-folding membrane structure as a one-dimensional structure and analyzed it based on the curved elastic beam theory. Xia et al [30,31], Satou et al [22], and Dharmadasa and Jiménez [3] also proposed several beam-theory-based models for the Z-folding structure. Schenk et al [23,14,10,33] used the so called barhinge method that analyzes the origami structure as an equivalent pin-jointed truss frame.…”