Large Displacements and the Stiffness of a Flexible Shell

Abstract

The design of static thin shell structures can be carried out using analytical and numerical approaches. Recently, thin shells have been studied for their flexibility, which can be beneficial for adaptive systems. However flexible systems involve large displacements and precise kinematics. The analysis of flexible shell systems is challenging due to the nonlinearities induced by these large displacements. This study addresses the nonlinear behaviour and stress-stiffening effects caused by large displacements in a 0.80 m-long carbon fibre reinforced plastic shell consisting of two monolithically connected lobes. The structural behaviour of this system is investigated both numerically and experimentally. Following the analysis framework, the non-linear effects of the large displacements on the shell stiffness are numerically determined using eigenvalue analysis and the displacement response to external loading on deformed shell configurations. The numerical displacement results are compared with results obtained in the experimental study. In conclusion, our study shows that the stiffness of the shell system under study increases 113% during deformation. More precisely, we establish that this change in stiffness is governed by the presence of tensile stresses in the shell surface due to deployment rather than by the change of the system's geometry.

Effect of Gravity on the Scale of Compliant Shells

“…This non-dimensional number is significant because it unifies the behavior of shells across scales. This outcome is in line with the bio-inspiration approach that distills geometries of a plant or micro-scale shell and scales them up for engineering applications [1,16]. As long as the ratio of characteristic dimension R over thickness H is kept high, the mechanical behavior of the compliant shell is similar at the large engineered scale and the observed biological scale.…”

“…This In accordance with Equation (8), the gravitational force is larger (in magnitude) as the scale of the shell increases. This is appears in Figure 4 with thin shell of larger characteristic dimensions having low values of G i such as for example façade shading shells [16,17,28]. Shells with a characteristic dimension R lower than 0.1 m tend to have Gi > 1.…”

“…For instance, the adaptive air inlet for aeronautic applications described in [12] must be able to function under any orientation of the airplane. In contrast, a compliant shell for adaptive shading of buildings does not have the same constraints as it operates in a position aligned with gravity's vertical orientation and can therefore be up scaled to larger sizes [16][17][18].…”

“…The ideal behavior for a thin shell used as a mechanism is characterized by a small actuation force that results in both bending deformations and preservation of the smoothness of the surface (i.e., no crumpling or wrinkling). This force can only be made small if it activates is low stiffness deformation mode of the shell [16]. This ideal behavior occurs if the shell is stiff enough to have a bending stiffness that preserve the continuity of the material under loading and flexible enough to allow large elastic out-of-plane deformation.…”

“…While biologically compliant shells appear at the smallest of the 10 length scales cited above, the use of those structures in biology has started to inform the design of engineered mechanisms at larger scales. Examples of flexible shells observed in nature have inspired engineered scale adaptive structures [15][16][17][18] at the meter scale, but the question of whether such structures could be scaled up even further still remains open and drives this study. This succinct literature review shows that there is a clear gap of knowledge as to what the limiting scale of compliant shells is and what the defining parameter is that determines this scale.The main hypothesis guiding this study is that the lack of large-scale compliant shells is due to the limiting effect of gravity-induced body forces on the shell's movements.…”